01 - In a 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, allowing 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. Cover with plastic wrap or damp towel and let rise in a warm, draft-free place for 1 to 1.5 hours, or until doubled in size.
05 - Punch down risen dough to release air. Divide into 12 equal pieces and shape each into a smooth, tight ball by tucking edges underneath.
06 - Arrange dough balls in a greased 9x13-inch baking pan or on a parchment-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 during the final 15 minutes of the second rise.
08 - Whisk together egg and milk for the egg wash. Gently brush the tops of each roll with the mixture, being careful not to deflate the dough.
09 - Bake for 18-22 minutes until rolls are deep golden brown and sound hollow when tapped on the bottom. Rotate pan halfway through for even browning.
10 - Let rolls cool in the pan for 5-10 minutes before transferring to a wire rack. Serve warm or at room temperature.