01 - In stand mixer bowl, combine flour, sugar, yeast, and salt. Mix briefly to distribute evenly.
02 - Add eggs and lukewarm milk. 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 absorbed before adding the next. Continue kneading for 8–10 minutes until dough becomes smooth, elastic, and pulls away from bowl sides.
04 - Transfer dough to lightly greased bowl, turning to coat. Cover with plastic wrap or damp towel. Let rise in warm, draft-free place for 1–1.5 hours until doubled in size.
05 - Punch down risen dough to release air. Divide into 12 equal portions. Shape each into smooth, taut ball by pulling edges underneath and rolling against work surface.
06 - Arrange dough balls in greased 9x13-inch baking pan or on parchment-lined baking sheet, spacing slightly apart. Cover and let rise 45–60 minutes until puffy and noticeably expanded.
07 - Preheat oven to 350°F with rack in center position.
08 - Whisk egg and milk until combined. Brush tops of rolls gently with egg wash, being careful not to deflate dough.
09 - Bake for 18–22 minutes until deep golden brown and rolls sound hollow when tapped on bottom. Rotate pan halfway through for even browning.
10 - Let rolls cool in pan for 5–10 minutes before transferring to wire rack. Serve warm or at room temperature.