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Step 1
Make the Dough: Combine the water and yeast in the bowl of a stand mixer (or a mixing bowl, if kneading by hand). Add the flour and the salt. Stir with a wooden spoon until a shaggy dough is formed.
Step 2
Fit the mixer with a dough hook attachment and knead the dough at low speed until the dough is slightly tacky but smooth, 3 to 5 minutes. If the dough sticks to the sides of the bowl, add 1 tablespoon of flour at a time and knead until the dough is smooth. If the dough feels very stiff and dry, add 1 tablespoon of water at a time and knead until the dough is smooth.
Step 3
Transfer the dough to a clean bowl that has been lightly greased with butter, turning the dough to coat it with butter. Cover the mixing bowl with plastic wrap and let the dough rise until doubled in size, about 1 hour.
Step 4
Once the dough has doubled in size, place it in the refrigerator for at least 30 minutes. [MAKE-AHEAD NOTE: At this point, you can refrigerate the dough overnight, then proceed with the recipe.]
Step 5
Make the Butter Block: Beat the butter on low speed until it’s homogeneous and waxy in texture, about 3 minutes, scraping the beater and bowl as needed to break up the cubes. Turn the butter out onto a piece of parchment paper and shape into a rectangle about 6 inches by 10 inches. Wrap up the butter in the parchment paper, pressing out any air. Gently roll a rolling pin over the butter packet, pushing the butter into the corners to create a perfect rectangle with even thickness. Refrigerate until firm yet still pliable, about 25 to 30 minutes.
Step 6
Roll out the Dough: Place the chilled dough onto a floured work surface and roll into a rectangle 12 inches by 20 inches. Remove the butter from the refrigerator and place it in the middle of the dough. Fold one half of the dough over the butter, then fold the other half on top, like folding a letter. Roll it out slightly to press the layers together, then fold it again into thirds like a letter.
Step 7
“Turn the Dough” #1: Rotate the dough so that the open, narrower edge is facing you. Roll the dough out to a rectangle 12 inches wide by 20 inches long. Fold the top third down and bottom third up, again like folding a letter. Place the packet of dough on a baking sheet, cover with plastic wrap, and refrigerate for 30 minutes.
Step 8
“Turn the Dough” #2: Place the packet of dough on a floured surface with the open, narrower edge facing you. Roll the dough out to a rectangle 12 inches wide by 20 inches long. Fold the top third down and bottom third up, again like folding a letter. Place the packet of dough on a baking sheet, cover with plastic wrap, and refrigerate for 30 minutes. [MAKE-AHEAD NOTE: At this point, you can wrap the dough in plastic wrap, place in a freezer-safe bag and freeze for up to 2 months. Thaw in the refrigerator overnight, then proceed with the recipe.]
Step 9
“Turn the Dough” #3: Place the packet of dough on a floured surface with the open, narrower edge facing you. Roll the dough out to a rectangle 12 inches wide by 20 inches long. Sprinkle the entire surface of the dough with ¾ cup of the sugar, then press lightly to help it stick to the dough. Fold the top third down and bottom third up, again like folding a letter. If any sugar falls out, press it back into the folds. Place the packet of dough on a baking sheet, cover with plastic wrap, and refrigerate for 30 minutes.
Step 10
“Turn the Dough” #4: Place the packet of dough on a floured surface with the open, narrower edge facing you. Roll the dough out to a rectangle 12 inches wide by 20 inches long. Sprinkle the entire surface of the dough with ¾ cup of the sugar, then press lightly to help it stick to the dough. Fold the top third down and bottom third up, again like folding a letter. If any sugar falls out, press it back into the folds. Place the packet of dough on a baking sheet, cover with plastic wrap, and refrigerate for 30 minutes.
Step 11
Prepare the Muffin Tin: Grease the insides of a standard 12-cup muffin pan generously with butter. Set aside.
Step 12
Shape the Kouign-Amann: Sprinkle the work surface with sugar. Remove the dough from the refrigerator and transfer it to the counter. Sprinkle a little additional sugar over the top of the dough. Roll the dough out to a rectangle 8 inches wide by 24 inches long.
Step 13
Slice the dough down the length to form two strips that are 4 inches wide by 24 inches long. Cut each strip into 4-inch squares to create 12 squares. Fold the corners of each square toward the center. Pick up each pastry and tuck it firmly into the muffin pan; it will feel like you’re squishing the pastry in there! [MAKE-AHEAD NOTE: At this point, you can cover the pan with plastic wrap and refrigerate overnight. The next day, allow the pastries to come to room temperature and rise for 1 hour before baking.]
Step 14
Cover the pan loosely with plastic wrap and let them rise until slightly puffy, 30 to 40 minutes.
Step 15
Meanwhile, preheat the oven to 400 degrees F.
Step 16
Bake the Kouign-Amann: Set the muffin pan on a rimmed baking sheet, place in the oven and immediately reduce the heat to 350 degrees F. Bake until the pastries are deep golden brown and tips are very dark brown, 40 to 45 minutes, rotating the pan halfway through baking.
Step 17
Transfer the pan to a cooling rack and let the pastries stand until they are just cool enough to handle, about 5 minutes. Gently remove them from the muffin pan and set them on the cooling rack to finish cooling completely. The kouign amann can be served warm or at room temperature. They are best served the same day they are made.