Warm the milk until just hot to the touch, then stir in sugar and yeast.
Let the mixture stand until foamy on top, about 5–10 minutes.
Combine flour and salt in a mixer bowl fitted with a dough hook.
Pour in the foamy milk and the beaten eggs. Mix on low until a rough dough forms.
Increase to medium speed and knead until smoother, about 3 minutes.
Add softened butter a tablespoon at a time, letting it fully incorporate.
Knead until the dough is glossy, stretchy, and cleans the bowl, 6–8 minutes.
Grease a bowl with oil, shape dough into a ball, and place seam-side down.
Cover and let rise in a warm spot until doubled, about 60–90 minutes.
Turn out the dough, gently deflate, and divide into 12 equal pieces.
Round each piece into a tight ball. Rest 10 minutes uncovered.
Arrange on a parchment-lined sheet or in a 9x13-inch pan, spaced evenly.
Cover and proof until puffy and nearly doubled, 45–75 minutes.
Preheat oven to 375°F. Brush rolls gently with milk.
Bake until deep golden and 195°F inside, about 16–18 minutes.
Brush hot rolls with melted butter. Cool 10–15 minutes before serving.