Place the milk and yeast in a small bowl; stir to dissolve.
Place the flour, salt, and eggs in the bowl of an electric mixer fitted with the dough hook attachment; add yeast mixture and mix on low speed to combine and knead, about 5 minutes. Scrape down sides of bowl with a spatula; knead on medium speed until smooth and elastic, about 10 minutes.
In a large bowl, mix together butter and sugar. Add a few small pieces of butter mixture to dough; with the mixer on low, add remaining butter mixture, a little bit at a time. When all the butter mixture has been added, increase speed and continue mixing until smooth, shiny, comes away from the sides of the bowl, and is elastic, 6 to 8 minutes.
Butter a large bowl, transfer dough to prepared bowl, and cover with plastic wrap; let stand in a warm place until doubled in volume, about 2 hours.
Lift dough from bowl and drop back into bowl to deflate; repeat process once or twice. Cover bowl and transfer to refrigerator to chill for at least 8 hours and up to overnight.
Butter two brioche molds that are 8 inches across the top and 3 1/2 inches across the bottom. Divide dough in half. Cut off one-quarter of each piece of dough; you should have two pieces that are about 15 ounces each, and two pieces that are about 5 ounces each.
Shape the large pieces into balls and place one piece in the bottom of each mold. Press two fingers into the center of each to make a deep indentation. Shape the small pieces of dough into a ball and roll each at an angle into an elongated oval. Lightly flour middle and index fingers on one hand and gently press the narrow ends of the ovals into the indentation in the large ball so that only the top parts are left visible.
In a small bowl, whisk together egg yolk and milk. Brush dough with egg yolk mixture, reserving remaining. Spray two pieces of plastic wrap with nonstick cooking spray; cover dough in both molds, cooking spray-side down and let stand in a warm place until doubled in volume, 1 1/2 to 2 hours.
Preheat oven to 400 degrees on a convection oven or 425 degrees on a conventional oven.
Working from the outside inward, brush each brioche very lightly with reserved egg yolk mixture. Using a pair of very sharp wet scissors, make five 1 ¼-inch deep cuts around the large pieces of dough on an angle. Transfer molds to oven and bake until brioche just begins to turn golden, about 15 minutes. Reduce temperature to 350 degrees on a convection oven or 375 degrees on a conventional oven and continue baking until deep golden brown and internal temperature reaches 205 degrees on an instant-read thermometer, 20 to 25 minutes more.
Remove from oven and let brioche cool in mold for 5 minutes. Unmold onto a wire rack and let cool completely.