Kouign-Amann

Instructions

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Whisk flour, yeast, and salt together in bowl of stand mixer. Whisk milk, 2 tablespoons sugar, and 2 tablespoons melted butter in 4-cup liquid measuring cup until sugar has dissolved. Using dough hook on low speed, slowly add milk mixture to flour mixture and mix until cohesive dough starts to form and no dry flour remains, about 2 minutes, scraping down bowl as needed. Increase speed to medium-low and knead for 1 minute. Cover bowl tightly with plastic wrap and let dough rest for 30 minutes.
Transfer dough to parchment paper–lined rimmed baking sheet and press into 9 by 6-inch rectangle, about 1 inch thick. Wrap tightly with greased plastic and refrigerate for 2 hours.
Meanwhile, fold 24-inch length of parchment in half to create 12-inch rectangle. Fold over 3 open sides of rectangle to form 6-inch square with enclosed sides. Crease folds firmly. Place chilled butter directly on counter and beat with rolling pin until butter is just pliable but not warm, about 60 seconds, then fold butter in on itself using bench scraper. Beat into rough 6-inch square.
Unfold parchment envelope. Using bench scraper, transfer butter to center of parchment, refolding at creases to enclose. Turn packet over so that flaps are underneath, and gently roll until butter fills parchment square, taking care to achieve even thickness. Refrigerate for at least 45 minutes.
Transfer dough to lightly floured counter and roll into 13 by 7-inch rectangle, with long side parallel to counter edge. Unwrap butter square and place in center of dough. Fold 2 sides of dough over butter so they meet in center. Press seam together with your fingertips.
Using rolling pin, press firmly on each open end of packet. Roll dough into 18 by 6-inch rectangle, with short side parallel to counter edge. Fold bottom third of dough over middle, then fold upper third over it like business letter to form 6-inch square. Turn dough 90 degrees counterclockwise and repeat rolling and folding into thirds. Return dough to parchment-lined sheet, wrap tightly with greased plastic, and return to refrigerator for 30 minutes.
Sprinkle 2 tablespoons sugar into rough 6-inch square on clean counter. Place dough on top of sugar so that top flap of dough is facing right, and sprinkle evenly with 2 tablespoons sugar.
Roll into 18 by 6-inch rectangle, with short side parallel to counter edge, gently flipping dough and redistributing sugar on counter as needed.
Fold bottom third of dough over middle, then fold upper third over it like business letter to form 6-inch square. Turn dough 90 degrees counterclockwise and repeat rolling and folding into thirds with ¼ cup sugar. Return dough to parchment-lined sheet, wrap tightly with greased plastic, and refrigerate for at least 2 hours or up to 24 hours. (Some moisture may appear around seams.)
Grease 12-cup muffin tin with 1 tablespoon melted butter. Coat bottom and sides of muffin cups with 2 tablespoons sugar and tap out excess.
Transfer dough to lightly floured counter so that top flap of dough is facing right. Roll dough into 16½ by 12½-inch rectangle, with short side parallel to counter edge, gently flipping dough and reflouring counter as needed.
Using pizza cutter or chef’s knife, trim ¼ inch of dough from each edge and discard. Reshape dough as needed; remaining rectangle should measure 16 by 12 inches. Cut dough vertically into 3 (16 by 4-inch) strips, then cut horizontally into twelve 4-inch squares.
Spread ¼ cup sugar onto bottom of shallow dish. Working with 1 dough square at a time, coat both sides with sugar, pressing gently to adhere. Fold four corners of square into center and press firmly on pointed ends to seal.
Place squares into muffin cups, folded side up, pressing dough gently into corners. Cover loosely with greased plastic and let rise until nearly doubled in size, 2½ to 3 hours. (Unrisen kouign-amann can be refrigerated for up to 18 hours; let rise at room temperature for 3 to 3½ hours before baking.)
Adjust oven rack to middle position and heat oven to 350 degrees. Gently press down on any pointed ends in center of kouign-amann that have become unsealed. Brush tops with remaining 1 tablespoon melted butter and sprinkle with remaining 2 tablespoons sugar and sea salt, if using.
Bake until deep golden brown, 25 to 30 minutes, rotating muffin tin halfway through baking. Let kouign-amann cool in muffin tin for 3 minutes, then invert individually onto wire rack and let cool, still inverted, for 10 minutes. Serve warm or at room temperature.