In a small microwave-safe bowl, stir together 3 tablespoons (45 grams) water and ½ teaspoon (2 grams) sugar; heat on high in 10-second intervals until an instant-read thermometer registers 110°F (43°C) to 115°F (46°C). Whisk in yeast until well combined. Let stand until foamy, 5 to 10 minutes.
In the bowl of a stand mixer fitted with the paddle attachment, beat bread flour, salt, and remaining 2 tablespoons plus 2½ teaspoons (34 grams) sugar at low speed until combined. Add 3 tablespoons (42 grams) cold butter; beat until mixture resembles coarse bread crumbs, about 3 minutes. Add remaining ½ cup (113 grams) cold butter; beat just until butter is coated with flour.
Add cold milk to yeast mixture. With mixer on low speed, add yeast mixture to flour mixture in a slow, steady stream, beating just until a shaggy dough comes together. (There will still be large pieces of butter.)
Lightly dust work surface with all-purpose flour. Turn out dough onto prepared surface, and shape into a rough 5-inch square. (Dough will be soft and slightly sticky.) Wrap in plastic wrap, and freeze for 30 minutes.
Lightly dust work surface with all-purpose flour. Turn out dough onto prepared surface, and roll into a 10×5-inch rectangle, lightly dusting surface and top of dough with all-purpose flour as needed. (See Note.) Fold dough in half so short sides meet. Pat fold to mark center. Unfold dough, and pull one short side to center. Pull opposite side to center so short sides are touching. Pinch seams together; fold along center seam, like closing a book. (This is called a book-fold.) Rotate dough 90 degrees; repeat rolling and folding procedure once to complete second book-fold. (Dough will start out soft, rough, and somewhat sticky but will come together; turn dough over as needed so edges are rolled out as evenly as possible.) Wrap in plastic wrap, and freeze for 15 minutes.
Repeat rolling, folding, and rotating procedure twice (a total of 4 book-folds). Wrap dough in plastic wrap, and refrigerate for at least 1½ hours or up to overnight.