Combine the flour, milk, sugar, egg yolks, yeast, and salt in the bowl of a stand mixer. Install the paddle attachment and mix on low speed for 5 minutes until combined. Rest the dough for 15 minutes, then switch out the paddle for the dough hook.
Add half of the softened butter. Set mixer to low speed for 30 seconds then slowly increase to medium and mix until the dough pulls away from the sides of the bowl, 5 to 8 minutes. (At this point you should be able to pinch off a small piece of dough and work it into a thin sheet you can almost see through without tearing.)
Turn the dough out onto a work surface and roll and shape with your hands to form a smooth ball. Return the dough to the bowl, cover with plastic wrap, and stash in a warm spot to rise until doubled in size, about 1 hour.
Meanwhile, set the oven to 275°F and place a rack in the middle position. Grease a 9-by-13 inch metal baking pan with nonstick cooking spray.
Remove the dough from the bowl and use a bench scraper to cut the dough into 14 (2-ounce) portions. Roll each portion on the counter until it tightens into a small ball. Place in the greased pan, cover with plastic wrap, and set aside in a warm, dry place to rise until the rolls have doubled in size, 30 to 45 minutes.
Melt the remaining butter and gently brush it across the tops of the risen rolls. Bake until the rolls are set and reach an internal temperature of 185 to 190°F, about 25 minutes. They should be fairly pale on top.
Cool the rolls, still in the pan, on a cooling rack for 10 minutes. De-pan the rolls, keeping them right-side up, and cool to room temperature, 30 to 40 minutes. Wrap the rolls tightly in plastic wrap, then seal in a gallon-sized freezer zip-top bag. Freeze up to 3 months.
When ready to bake, remove the rolls from the bag and park at room temperature for 1 hour. Meanwhile, heat the oven to 400°F. When ready, move the rolls to a parchment-lined sheet pan and bake, rotating the pan halfway through baking, until the rolls are deeply browned, 10 to 12 minutes.
Wrap loosely in a clean tea towel to hold for service.