Place milk and yeast in a small bowl; stir to dissolve.
Place 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 10 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 16 mini brioche molds measuring 3 1/2 inches across tops and 2 inches across bottoms. Place on a baking sheet. Divide dough into 16 equal pieces, each about 2 1/2 ounces. Cut 1/2-ounce pieces from each piece of dough and set aside.
Shape large pieces into balls and place one piece in bottom of each mold. Press two fingers into the centers to make deep indentations. Shape small pieces of dough into balls and roll them at an angle into an elongated oval. Lightly flour a finger and gently press narrow ends of ovals into indentations in the large balls so that only top parts are left visible.
In a small bowl, whisk together egg yolk and milk. Brush dough with egg yolk mixture, reserving remaining. Spray a piece of plastic wrap with nonstick cooking spray; cover dough, cooking spray-side down and let stand in a warm place until doubled in volume, 1 to 1 1/2 hours.
Preheat oven to 400 degrees (if using a convection oven; 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 scissors make four to five 1 1/4-inch deep cuts around the large pieces of dough. Transfer molds to oven and bake until brioche just begins to turn golden, about 5 minutes. Reduce temperature to 350 degrees (on a convection oven; 375 degrees on a conventional oven) and continue baking until deep golden-brown and internal temperature reaches 205 degrees on an instant-read thermometer, 5 to 10 minutes more.
Remove from oven and let brioche cool in mold for 5 minutes. Unmold onto a wire rack and let cool completely.