In the bowl of your stand mixer with dough hook attached, add flour, salt, sugar, yeast, 2 eggs plus 2 yolks and warmed milk. Mix on low until a rough dough comes together.
Cut your room temperature butter into about 5 equal pieces, and with the mixer running on low, add the butter chunks one at a time. Do not add the next piece until the previous has been thoroughly mixed into the dough. Repeat until all butter is incorporated in.
Mix dough until smooth, and passes the window pane test. As this is a very enriched dough, kneading could take anywhere from 15-30 minutes. I leave my mixer going and check on the dough every 7-10 minutes.
When the dough is ready, place into a very lightly greased bowl, cover and allow to rise in a warm place for 90-120 minutes.
Line an 9x13 baking pan with parchment and set aside.
When your dough is ready, punch down and transfer to your work space.
Using a knife or a bench scraper, divide your dough into 12 equal portions. Cover the dough while you work on shaping each piece.
Taking one piece of the dough, place in your palm and take the edges of the dough, folding them in towards the center. Once you have pulled all the sides in, pinch the center together and place the dough ball, seam side down, onto the counter. Lightly cup your hand over the dough ball and using a circular motion move the dough to create tension. Place your shaped roll into your prepared baking pan. Repeat steps with remaining dough.
Cover your baking pan with your shaped dinner rolls and allow to rise for another 45-90 minutes in a warm place. Rolls are sufficiently proofed when they have puffed up considerably.
Preheat your oven to 350°F
Take the egg whites you reserved and brush the tops of your rolls.
Place your baking pan on the center rack of your oven and bake your rolls for about 25 minutes. The bread will be a deep brown color when they are ready.
Remove from the oven and allow bread to cool for at least 20 minutes before enjoying. Store bread in an airtight container.
