01 - Combine flour, sugar, yeast, and salt in stand mixer bowl. Mix briefly to distribute evenly.
02 - Add eggs and lukewarm milk to dry ingredients. Mix on low speed until a rough, shaggy dough forms.
03 - With mixer on medium speed, add softened butter one cube at a time, waiting for each piece to fully incorporate before adding the next. Continue kneading for 8–10 minutes until dough becomes smooth, shiny, and elastic.
04 - Transfer dough to a lightly greased bowl, turning to coat all sides. Cover with plastic wrap or damp towel and let rise in a warm, draft-free area for 1–1.5 hours until doubled in volume.
05 - Punch down dough to release air. Divide into 12 equal portions and shape each into a smooth, taut ball by tucking edges underneath.
06 - Arrange dough balls in a greased 9x13-inch baking pan or on a parchment-lined baking sheet, leaving slight space between each. Cover and let rise for 45–60 minutes until puffy and noticeably expanded.
07 - Preheat oven to 350°F.
08 - Whisk egg and milk together until combined. Gently brush tops of risen rolls with egg wash using light strokes to avoid deflating.
09 - Bake for 18–22 minutes until rolls are deeply golden brown and sound hollow when tapped on the bottom. Internal temperature should reach 190°F.
10 - Let rolls cool in pan for 10 minutes before transferring to wire rack. Serve warm or at room temperature.