Step 1

If using compressed yeast, finely crumble it into the bowl of a heavy-duty standing mixer. Add the sugar and let it rest until the yeast gives off some moisture, about 3 minutes. Whisk well to dissolve the yeast, then stir in the milk. If using active dry yeast, sprinkle the yeast over 1/4 cup of the milk that you've warmed to 105° F to 115° F (40°C to 46°C). Let it rest until the yeast softens and begins to foam, about 5 minutes. Whisk well to dissolve. Pour into the bowl of a heavy-duty stand mixer and then stir in the sugar. Add the remaining 1 cup cold milk.

Step 2

Mix the bread and pastry flours together. Add 2 cups of the flour mixture and the salt to the yeast mixture in the bowl. Attach the bowl to the mixer and fit it with the paddle attachment. Mix on low speed, adding enough of the remaining flour mixture as it takes to make a soft, sticky dough. Do not overmix, as the dough will be worked and absorb more flour during the rolling and folding processes.

Step 3

Move the dough to a floured work surface and knead a few times to smooth the surface. Shape the dough into a ball. The ball will hold its shape but will spread slightly as it stands.

Step 4

Dust a half-sheet pan with flour. Place the dough on the flour and use a small, sharp knife to cut an X about 1-inch (25-mm) deep in the top, marking it into quadrants. Sprinkle the top with a little flour and refrigerate.

Step 5

Clean the mixer bowl and paddle attachment. Add the butter to the bowl and beat with the paddle attachment on medium speed until the butter is almost smooth, about 30 seconds. Add the flour and continue beating until the mixture is smooth, cool, and malleable, about 30 seconds more. This is your beurrage (beurre = butter in French).

Step 6

Transfer the beurrage to a lightly floured work surface and press any remaining lumps of butter out with the heel of your hand. Shape the beurrage into a 4-inch (10-cm) square, place it on the half-sheet pan with the detrempe, and refrigerate for about 15 minutes. The detrempe and the beurrage should be the same consistency and temperature after this slight chilling.

Step 7

Flour the work surface again. Place the detrempe on the work surface with the ends of the X at approximately 2, 4, 7, and 10 o'clock positions. You will notice 4 quadrants of dough between the crosses of the X at the north, south, east, and west positions. Dust the top with flour. Using the heel of your hand, flatten and stretch each quadrant out about 2 1/2 inches (7 cm) to make a cloverleaf shape with an area in the center that is thicker than the "leaves."

Step 8

Use a rolling pin to roll each "cloverleaf" into a flap about 6-inches (15-cm) long and 5-inches (13-cm) wide, leaving a raised square in the center. Using the side of the rolling pin, press the sides of the raised area to mark the square.

Step 9

Place the butter square in the center of the cloverleaf. Gently stretch and pull the north-facing flap of dough down to cover the top and sides of the butter square, brushing away any excess flour. (This dough is very extendable and will stretch easily but you do need to be a little careful not to tear it. If you do, simply try to pat it back together again.)

Step 10

Now stretch and pull the south-facing flap up to cover the top and sides of the butter square. Turn the packet so the open ends of the square face north and south. Repeat folding and stretching the north- and south-facing flaps (originally the east and west flaps) to completely cover the butter square, making a butter-filled packet of dough about 6-inches square.

Step 11

Dust the work surface with flour. Turn the packet over so the 4 folded flaps face down with the open seam facing you. Dust the top with flour. Using a large, heavy rolling pin held at a slight angle, lightly pound the top to widen it slightly and help distribute the butter inside. Roll the dough into a 17-by-9-inch (43-by-23-cm) rectangle. Fold the dough into thirds, like a business letter, brushing away any excess flour. This is called a single turn. Roll the rectangle lightly to barely compress the layers. Transfer to a half-sheet pan and refrigerate for about 20 minutes.

Step 12

Lightly flour the work surface. Place the dough on the work surface with the long open seam facing you. Dust the top with flour. Roll out the dough into a 17-by-9-inch rectangle. Fold the right side of the dough over 2 inches (5 cm) to the left. Fold the left side of the dough over to meet the right side. Fold the dough in half vertically from left to right. This is a double turn (also known as a book turn). Roll the rectangle lightly to barely compress the layers. Return to the half-sheet pan and refrigerate for another 20 minutes.

Step 13

Repeat the last rolling and folding into a final single turn. With the long seam facing you, cut the dough in half vertically. Wrap each piece tightly in plastic wrap, then wrap again. Freeze for at least 24 hours or up to 4 days. The night before using the dough, place it in the refrigerator and let thaw overnight, about 8 hours. Once defrosted the dough will begin to rise, so make sure to roll it out immediately.

Step 14

Line 2 half-sheet pans with parchment paper. Dust your work surface with flour. Place the dough on the work surface with the open seam facing you. Dust the top with flour. Using a large, heavy rolling pin, roll out the dough into a 16-by-12-inch (40-by-30-cm) rectangle. Don't press too hard; let the weight of the pin do much of the work. If you change the position of the dough while rolling it, keep track of which side contains the seam.

Step 15

Turn the packet so the seam faces you. (If you've lost track, look carefully at the sides of the dough, and you should be able to discern it, even though it's faint.) Using a pizza wheel and a yardstick or rule, neatly trim the rough edges so you have a neat rectangle. Cut in half lengthwise to make two 16-by-6-inch (40-by-15-cm) rectangles. Fold each rectangle into thirds, place on a half-sheet pan, and refrigerate, uncovered, for about 15 minutes.

Step 16

Remove the dough from the refrigerator. Working with one piece of dough at a time, unfold it on the work surface. Using a pizza wheel and a yardstick, start at the top left corner of the dough and make your way downward diagonally to make a half-triangle with a 2-inch base. Measure 3 1/2-inches (9-cm) from the top left corner of the strip and mark this point with a notch from the wheel. Cut down diagonally from the notch to meet the bottom left edge of the dough strip to make another triangle with a 3 1/2-inch base. Continue cutting, alternating directions of your diagonal cuts, to cut out 6 triangles. The last cut will yield a half-triangle with a 2-inch-wide base. Repeat with the second strip of dough to make 6 more large triangles and 2 half-triangles. You should have a total of 12 large triangles and 4 half-triangles.

Step 17

(Because a picture says a thousand words, see the slideshow above.) To shape the croissants, place a single "complete" triangle on the work surface with the base of the triangle facing you. Stretch the bottom slightly so it is about 5-inches (13-cm) wide. Pick up the triangle. With one hand, hold the dough triangle at the bottom and stretch it with your other hand until it is about 7-inches (17-cm) long. Return the triangle to the work surface. Starting at the bottom, roll up the triangle, and finish with the tip underneath the croissants on the pan. Curve the croissants by bringing the 2 ends together and then cross one end over the other, and press together. Repeat rolling the remaining dough triangles, placing them 1 1/2-inches (4-cm) apart on the pan. Overlap 2 of the half-triangles at their long sides, and press the seam together. Roll up as described for the large triangles and add to the pan. Repeat with the remaining half-triangles. [Editor's Note: Whew! You made it! Congrats!]

Step 18

Choose a warm place in the kitchen for proofing. Slip each pan into a tall plastic bag. Place a tall glass of very hot water near the center of each pan. Wave the opening of each bag to trap air and inflate it like a balloon to create "head room," being sure that the plastic does not touch the delicate dough. Twist each bag closed. Let stand until the croissants look puffy but not quite doubled in size, 1 1/2 to 2 hours.

Step 19

Meanwhile, position racks in the center and top third of the oven and preheat to 375°F (190°C). Remove the glasses from the bags, then the pans. Lightly brush the croissants with the beaten egg. Bake for 10 minutes. Reduce the heat to 350°F (176°C) and continue baking until the croissants are crisp and golden brown, about 15 minutes longer. Serve the croissants warm or at room temperature.