Warm the milk until just lukewarm to the touch.
Bloom the yeast by stirring milk with sugar and honey, then sprinkle yeast on top. Rest 5–10 minutes.
Whisk in the melted butter and beaten egg until smooth.
Combine flour and salt in a bowl. Add to the liquids gradually, stirring until a shaggy dough forms.
Knead the dough on a lightly floured surface until smooth and springy, about 8–10 minutes.
Place dough in a greased bowl, cover, and let rise until doubled, 50–70 minutes in a warm spot.
Punch down the dough and roll it to about 1/2 inch thick.
Cut into 16 even squares or rectangles. Arrange on a lined baking sheet, spaced slightly apart.
Cover and proof until puffy, 20–30 minutes. Preheat the oven to 350°F.
Bake until golden on top and set, 12–15 minutes.
Brush warm rolls generously with melted butter. Let cool slightly before serving.