In the bowl of a stand mixer, whisk together milk, egg, egg yolk, and yeast by hand; add flour, sugar, 3 tablespoons (42 grams) butter, and salt. Using the dough hook attachment, beat at low speed until dough comes together, about 1 minute; beat until dough pulls away from sides of bowl and is smooth when a small amount is pinched off, 5 to 8 minutes. Turn out dough onto a lightly floured surface, and shape into a smooth ball.

Spray a large bowl with cooking spray. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, about 2 hours.

Line a baking sheet with parchment paper. Lightly dust parchment with flour.

Turn out dough onto a lightly floured surface, and gently shape into a 10x8-inch rectangle. Place on prepared pan. Cover tightly with plastic wrap, and refrigerate overnight.

In a small bowl, stir remaining 1 cup plus 1 tablespoon (241 grams) butter with a small spatula until soft and creamy.

Freeze dough for 15 to 30 minutes.

On a very lightly floured surface, roll dough into an 18½-inch square. Using a sharp knife, trim ¼ inch from all sides. Using a small offset spatula, spread butter evenly onto dough. Using a ruler, carefully score buttered surface of dough, marking dough into 9 (6-inch) squares. (Do not cut through dough.)

Using a sharp knife, in bottom third of dough, carefully make a 6-inch cut to the left and the right scoring of dough; repeat cuts in top third of dough. Working from left to right and bottom to top, carefully fold marked squares, one onto another until dough is a 6-inch square and about 1¾ inches thick. Wrap dough in plastic wrap, and refrigerate for 1½ hours or freeze for 20 to 30 minutes.

On a lightly floured surface, roll dough into an 18x12-inch rectangle (about ⅛ inch thick). Fold in thirds like a letter. Wrap dough in plastic wrap, and refrigerate for 1½ hours or freeze for up to 3 months. Let frozen dough thaw overnight in refrigerator before using.