Step 1

Stir the water, yeast, and a pinch of the sugar together in a small bowl; set aside.

Step 2

In the bowl of a stand mixer fitted with the dough hook, whisk the milk, cream, egg yolk, salt, and remaining sugar together.

Step 3

Add the flour then turn the mixer on low speed and gradually pour the yeast mixture into the flour.

Step 4

Continue to beat on low until the flour is incorporated, stop and scrape down the sides and bottom as needed. Continue beating until the dough is smooth and elastic, about 20 minutes. Cover and refrigerate for 30 minutes.

Step 5

Meanwhile, pound the butter between 2 pieces of parchment paper into an 8-inch square. Make sure the butter is in an even layer. Place the butter into the refrigerator to firm up.

Step 6

Generously flour your work surface and turn the dough out. Roll the dough out into a 9x18 rectangle.

Step 7

Place the chilled square of butter on one half of the dough and fold the other half of the dough up over the butter so you end up with a square.

Step 8

Gently roll the dough with the butter inside into another rectangle. Fold the rectangle like a letter so you have 3 layers, starting with the narrow end. Wrap in plastic wrap and refrigerate for 30 minutes. This is the first turn.

Step 9

Turn the dough so the long sides are on your left and right. Roll the dough into another rectangle about the same size then fold it the same way as the previous step. Wrap in plastic wrap and refrigerate for 30 minutes to 1 hour. Repeat this process until you have made 4 turns.

Step 10

Wrap the dough in plastic wrap and refrigerate it for 12-24 hours. The dough must be shaped and proofed within 24 hours.

Step 11

Line 2 baking sheets with parchment paper. Cut the dough in half and roll each half into a 6x12 inch rectangle.

Step 12

Transfer each rectangle to its own prepared baking sheet. Trim the edges so they are even and refrigerate for 20 minutes. The dough should be firm but not brittle.

Step 13

Use a large knife to cut each rectangle into 6 triangles. Make a small cut at the center of the base on each triangle.

Step 14

Begin rolling up the croissants, curling the two side fo the triangle on each side of the cut away from each other. Continue to roll with both hands until the tip is underneath. Bend the 2 ends toward each other in the shape of a crescent.

Step 15

Arrange the croissants on the baking sheets, cover them with plastic wrap and set them in a warm place to rise until they've doubled in size, about 1 hour.

Step 16

Preheat the oven to 375°F. Beat the egg and egg yolk together until well broken up and brush the egg wash over the tops of each croissant.

Step 17

Bake for 35 minutes or until puffed and golden brown. Cool on a wire rack to room temperature before serving.