How to Make It
Stir together flour, 1/4 cup sugar, and salt in a medium bowl; set aside. Stir together 2/3 cup warm water, yeast, and remaining 1 teaspoon sugar in the bowl of a stand mixer fitted with a dough hook. Let stand until foamy, about 5 minutes. Meanwhile, place 3 tablespoons butter in a microwavable bowl, loosely cover with a paper towel, and microwave on high until melted, about 30 seconds. (Keep remaining butter refrigerated.) Add melted butter and milk to yeast mixture. With mixer running on low speed, gradually add flour mixture to yeast mixture, beating until dry ingredients are incorporated, about 6 minutes. Increase speed to medium-low, and beat until dough is smooth, elastic, and tacky, about 8 minutes. Shape dough into a ball; flatten slightly. Place dough on a lightly floured large plate; wrap tightly in plastic wrap. Refrigerate at least 2 hours or up to 8 hours or overnight for more flavor.
Place remaining 1 1/2 cups cold butter between 2 sheets of parchment paper; let stand at room temperature 10 minutes. Using a rolling pin, pound butter to flatten and soften slightly. Removing and replacing parchment as needed, use a bench scraper and a rolling pin to shape butter into a 7 1/2-inch square block of even thickness. Refrigerate between sheets of parchment paper 15 minutes.
Unwrap chilled dough, and transfer to a lightly floured surface. Lightly flour top of dough. Roll into a 12-inch square; brush off excess flour. Remove and discard top sheet of parchment paper from butter block. Using bottom sheet of parchment paper as handles and turning butter block 45 degrees, flip butter onto middle of dough square. (Butter will be in a diamond shape, leaving corners of dough square exposed.) Remove and discard parchment paper. Using a rolling pin and starting at edge of butter block, roll each dough corner away from the center until it is 8 inches long (about 1/16 inch thick), flouring as needed. Brush off excess flour. Fold one elongated dough corner up and over butter block, stretching gently into a square to fully cover butter. Repeat with remaining dough corners, creating 4 layers of thinly stretched dough covering butter block.
Lightly flour work surface if needed. Press rolling pin across dough to create trenches, evenly dispersing butter. Roll dough into a smooth 24- x 12-inch rectangle. Starting with one short side, fold dough into thirds, like a letter. Transfer to a lightly floured baking sheet. Cover tightly with plastic wrap, and refrigerate until firm, about 45 minutes. Repeat rolling, folding, and chilling process 2 times. Proceed with making Classic Croissants.