01 - In stand mixer bowl, combine flour, sugar, yeast, and salt. Mix briefly to distribute evenly.
02 - Add eggs and lukewarm milk to dry ingredients. Mix on low speed until a shaggy dough forms.
03 - With mixer on medium speed, add butter one cube at a time, allowing each piece to fully incorporate before adding the next. Continue kneading for 8-10 minutes until dough is smooth, shiny, and elastic.
04 - Transfer dough to lightly greased bowl, turning to coat all sides. Cover with plastic wrap or damp towel. Let rise in warm, draft-free place for 1 to 1.5 hours until doubled in size.
05 - Punch down dough to release air. Turn onto lightly floured surface and divide into 12 equal portions. Shape each piece into smooth, taut ball by tucking edges underneath.
06 - Arrange dough balls in greased 9x13-inch baking pan or on lined baking sheet, leaving slight space between. Cover loosely and let rise 45-60 minutes until puffy and nearly doubled.
07 - Preheat oven to 350°F during final rise period.
08 - Whisk together egg and tablespoon milk until blended. Gently brush tops of risen rolls with egg wash for golden finish.
09 - Bake for 18-22 minutes until rolls are deep golden brown and sound hollow when tapped. Internal temperature should reach 190°F.
10 - Remove from oven and let cool in pan for 5-10 minutes. Transfer to wire rack. Serve warm or at room temperature.