Heat milk and 1⁄2 cup water to 115°. Stir in yeast; let sit until foamy, about 10 minutes.
Meanwhile, combine sugar, 12 yolks, and 4 tbsp. butter in the bowl of a standing mixer fitted with the whisk attachment. Beat on medium speed until smooth, about 2 minutes. Add yeast mixture and 1 cup flour; beat for 10 minutes. Remove bowl; cover with a damp kitchen towel. Set dough aside in a warm place to let rest, about 15 minutes.
Combine eggs and remaining yolks in a bowl. Return bowl of dough to mixer; replace whisk attachment with a dough hook. Working in 4 batches, beat in 1 1⁄2 cups flour, 3 tbsp. butter, and one-fourth of the egg mixture per batch on medium speed. Scrape down sides of bowl; remove bowl and cover with the towel; set dough in a warm place to let rest for 15 minutes.
Return bowl of dough to mixer; knead on medium speed while adding remaining butter in 4 batches. (Stop occasionally to scrape down dough hook.) Continue to knead until dough is elastic, 18–20 minutes.
Using your hands, grease a marble slab or other smooth surface with a little butter. Transfer dough to the greased work surface; divide into 10 equal pieces. Roll each piece into a ball; flatten each ball into a 6" circle. Fold edges of each circle in toward center. Transfer dough pieces, seam side down, onto 2 greased baking sheets. Cover with damp towels; set aside in a warm place to let rest for 10 minutes.
Line ten 5 1⁄2" fluted brioche molds with 9" circles of parchment paper. Divide molds between 2 baking sheets. Working with one dough piece at a time, use your hands to press it into a paper-thin, translucent square, about 14" x 14", on the greased surface. (The dough will tear in some places; that's okay.) Sprinkle the dough square with 2 tbsp. cheese. Starting at the edge closest to you, use your fingertips to roll the dough toward the far edge, forming a rope about 1⁄2" thick. Gently flatten the rope. Roll the rope into a spiral, tucking the end under. Transfer the spiral to a mold, tucked end down. Cover the molds with damp towels; set in a warm place to let rest until almost doubled in size, 1 1⁄2–2 hours.
Arrange a rack in the lower third of oven and heat to 350°. Sprinkle 1 tbsp. cheese over top of each risen dough. Bake breads, one baking sheet at a time, until golden brown and puffed, about 20 minutes. Let breads cool before unmolding.