Spray a half sheet pan with nonstick spray and set aside.
Place the milk, sugar, yeast, flour, egg yolks, and salt in the bowl of a stand mixer fitted with the paddle attachment. Combine on low speed for 1 minute. Change the paddle attachment to the dough hook and rest the dough for 10 to 15 minutes.
Add 2 ounces of the room temperature butter and mix on low speed. Increase the speed to medium and mix until the dough pulls away from the sides of the bowl and you are able to gently pull the dough into a thin sheet that light will pass through, about 8 minutes.
Turn the dough out onto a lightly floured work surface and roll and shape with hands to form a large ball. Return dough to the bowl, cover with plastic wrap, and set aside in a warm, dry place to rise until doubled in size, about 1 hour.
Remove the dough from the bowl and roll into a 16 by 3-inch log. Use a bench knife to cut the dough into 1 3/4-ounce portions, about 16 rolls. Using your loosely cupped hand, roll each portion on the counter until they tighten into small balls. Working 1 at a time, use a rolling pin to roll each small ball into a 3-inch circle or oval. Use the side of your hand or a small dowel to make an indentation across the middle of the circle. Place a small pat of chilled butter into the center of the indentation, then fold in half and gently press to seal the edges. Place the rolls, top-side down, onto the prepared sheet pan, spacing them evenly. Melt the remaining 1 ounce butter and brush the tops of the rolls. Cover with plastic wrap and set aside in a warm, dry place to rise until doubled in size, 30 to 40 minutes.
Preheat the oven to 400 degrees F.
Remove the plastic wrap and bake until the rolls reach an internal temperature of 200 degrees F, 8 to 10 minutes. Rotate the pan halfway through baking.
Remove the pan to a cooling rack and cool for 2 to 3 minutes before serving.