01 - Combine warm milk, sugar, and yeast in a large bowl. Let stand 5–10 minutes until foamy and activated.
02 - Whisk in melted butter, egg, and salt. Gradually add flour, mixing until a soft, sticky dough forms.
03 - Turn dough onto a floured surface. Knead for 7–8 minutes until smooth, elastic, and no longer sticky.
04 - Place dough in a greased bowl, turning to coat. Cover with plastic wrap and let rise in a warm, draft-free spot until doubled, about 1 hour.
05 - While dough rises, beat softened butter with minced garlic. Stir in mozzarella, Parmesan, parsley, and salt until combined.
06 - Punch down risen dough. On a floured surface, roll into a 12x16-inch rectangle.
07 - Spread garlic cheese mixture evenly over the dough, leaving a 1/2-inch border.
08 - Starting from a long edge, roll dough tightly into a log. Pinch seam to seal.
09 - Cut log into 12 equal slices. Place cut-side up in a greased 9x13-inch baking dish, leaving slight space between rolls.
10 - Cover loosely with towel. Let rise 25–30 minutes until puffy and nearly doubled. Preheat oven to 350°F during final 10 minutes.
11 - Bake 22–25 minutes until deeply golden brown and rolls sound hollow when tapped.
12 - Immediately brush hot rolls with melted butter. Sprinkle with parsley and Parmesan. Serve warm.