01 - In the bowl of a stand mixer, combine flour, sugar, yeast, and salt. Mix briefly to distribute evenly.
02 - Add eggs and lukewarm milk to the dry mixture. Mix on low speed until a rough, shaggy dough forms.
03 - With mixer on medium speed, add butter one cube at a time, waiting until each piece is fully incorporated before adding the next. Continue kneading for 8–10 minutes until dough is smooth, elastic, and pulls away from the sides of the bowl.
04 - Transfer dough to a lightly greased bowl, turning to coat all surfaces. Cover with plastic wrap or a clean towel and let rise in a warm, draft-free place for 1–1.5 hours until doubled in size.
05 - Gently punch down dough to release air. Turn onto a lightly floured surface and divide into 12 equal portions. Shape each piece into a smooth, taut ball by tucking the edges underneath.
06 - Arrange dough balls in a greased 9x13-inch baking pan or on a parchment-lined baking sheet, leaving slight space between rolls. Cover loosely and let rise for 45–60 minutes until puffy and nearly doubled.
07 - Preheat oven to 350°F.
08 - Whisk together egg and milk for the egg wash until well combined. Gently brush the tops of each roll with the mixture, being careful not to deflate the dough.
09 - Bake for 18–22 minutes until rolls are deep golden brown and sound hollow when tapped on the bottom. Rotate the pan halfway through baking for even browning.
10 - Remove from oven and let rolls cool in the pan for 5–10 minutes. Transfer to a wire rack to cool slightly longer, or serve warm.