Step 1: Make the Dough
In the bowl of a stand mixer, combine warm water and yeast. Let stand for 5 minutes until foamy. Add flour, 2 tablespoons sugar, salt, and softened butter. Using the dough hook attachment, mix on low speed for 2 minutes, then increase to medium speed and knead for 6-8 minutes until the dough is smooth and elastic. The dough should be slightly tacky but not sticky. If mixing by hand, knead on a lightly floured surface for 10-12 minutes.

Step 2: First Rise
Shape the dough into a ball and place in a lightly greased bowl. Cover with plastic wrap and let rise at room temperature for 1 hour until nearly doubled in size.

Step 3: Chill the Dough
Punch down the dough gently and shape it into a 6-inch square. Wrap tightly in plastic wrap and refrigerate for at least 2 hours or overnight. This rest is crucial for making the dough easier to roll and laminate.

Step 4: Prepare the Butter Block
While the dough chills, prepare your butter for lamination. Place the cold butter between two sheets of parchment paper. Using a rolling pin, pound and roll the butter into a 6-inch square that’s about ½-inch thick. The butter should be pliable but still cold. Refrigerate the butter square until ready to use.

Step 5: Begin Lamination (First Turn)
Remove the chilled dough from the refrigerator and place on a lightly floured surface. Roll it into a 12-inch square. Place the butter square diagonally in the center of the dough, like a diamond inside a square. Fold the four corners of the dough over the butter, meeting in the center and pinching the seams to seal completely. You’ve now enclosed the butter.

Step 6: First Sugar Turn
Sprinkle your work surface generously with ¼ cup of sugar (instead of flour). Roll the dough into a 12×18-inch rectangle. Sprinkle another ¼ cup of sugar evenly over the surface. Fold the dough in thirds like a business letter (bottom third up, top third down). Wrap in plastic wrap and refrigerate for 30 minutes.

Step 7: Second Sugar Turn
Unwrap the dough and place it on your work surface sprinkled with another ¼ cup of sugar, with the seam facing right (like a book you’re about to open). Roll again into a 12×18-inch rectangle. Sprinkle with another ¼ cup of sugar. Fold in thirds again. Wrap and refrigerate for at least 1 hour, or up to overnight.

Step 8: Final Roll and Shape
On a sugar-dusted surface, roll the dough into a 12-inch square, about ¼-inch thick. Trim the edges with a sharp knife or pizza cutter to create clean lines. Cut the dough into 12 equal squares (3 rows by 4 rows, each about 3×3 inches).

Step 9: Form the Pastries
Brush each cup of a muffin tin generously with melted butter, then coat with granulated sugar. Take one square of dough and bring all four corners to the center, pinching them together gently. Place in a prepared muffin cup, pinched side up. Repeat with remaining squares. Don’t worry if they look rustic—they’ll transform beautifully in the oven.

Step 10: Final Rise
Cover the muffin tin loosely with plastic wrap and let the pastries rise at room temperature for 45 minutes to 1 hour. They should look slightly puffy but won’t double in size.

Step 11: Bake
Preheat your oven to 350°F (175°C). Place a baking sheet on the lower oven rack to catch any sugar drips. Remove the plastic wrap from the muffin tin and bake for 25-30 minutes, until the kouign amann are deep golden brown with caramelized, crispy edges. They should look darker than you think—that’s the sugar caramelizing properly.

Step 12: Cool and Serve
Let the pastries cool in the tin for 2-3 minutes only—any longer and the caramelized sugar will cement them to the pan. Using a butter knife or small offset spatula, carefully loosen each pastry and transfer to a wire rack. If desired, sprinkle with a pinch of fleur de sel while still warm. Serve warm or at room temperature.