01 - In a stand mixer bowl, 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 softened butter one cube at a time, allowing each cube to fully incorporate before adding the next. Continue kneading for 8–10 minutes until dough is smooth, elastic, and pulls away from the bowl sides.
04 - Transfer dough to a lightly greased bowl. Cover with plastic wrap or a clean towel and let rise in a warm, draft-free place for 1 to 1 1/2 hours until doubled in size.
05 - Punch down the risen dough to release air. Divide into 12 equal portions and shape each into a smooth, taut ball by tucking the edges underneath.
06 - Arrange dough balls in a greased 9x13-inch baking pan or on a lined baking sheet, spacing slightly apart. Cover and let rise for 45–60 minutes until puffy and noticeably expanded.
07 - Preheat oven to 350°F.
08 - Whisk together egg and tablespoon of milk until combined. Gently brush the tops of the risen rolls with the egg wash mixture.
09 - Bake for 18–22 minutes until rolls are golden brown on top and sound hollow when tapped gently on the bottom.
10 - Let rolls cool in the pan for 5–10 minutes before serving warm.