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 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 is smooth, elastic, and pulls away from the bowl sides.
04 - Transfer dough to a lightly greased bowl, turning to coat all sides. Cover with plastic wrap or a clean towel and let rise in a warm, draft-free area for 1–1.5 hours until doubled in size.
05 - Gently punch down risen 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 nearly doubled.
07 - Preheat oven to 350°F.
08 - Whisk together egg and milk until combined. Gently brush the tops of each risen roll with the egg wash mixture for a glossy, golden finish.
09 - Bake for 18–22 minutes until rolls are deeply golden brown and sound hollow when tapped. If browning too quickly, tent loosely with foil after 15 minutes.
10 - Let rolls cool in the pan for 10 minutes before transferring to a wire rack. Serve warm or at room temperature.