01 - Combine warm milk, sugar, and yeast in a large bowl. Let stand for 5–10 minutes until mixture becomes foamy.
02 - Stir 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 and elastic, adding more flour only if necessary to prevent sticking.
04 - Place dough in a greased bowl, turning to coat all sides. Cover with plastic wrap and let rise in a warm, draft-free area until doubled in size, about 1 hour.
05 - While dough rises, combine softened butter, minced garlic, mozzarella, Parmesan, parsley, and salt in a medium bowl until well blended.
06 - Punch down risen dough and roll out on a lightly floured surface into a 12x16-inch rectangle.
07 - Spread cheese filling evenly over the dough, leaving a 1/2-inch border around the edges.
08 - Starting from one long edge, roll dough tightly into a log. Pinch seam to seal.
09 - Cut log into 12 equal slices using a sharp knife or dental floss. Place rolls cut-side up in a greased 9x13-inch baking dish.
10 - Cover dish with plastic wrap and let rolls rise for 25–30 minutes until puffy. Preheat oven to 350°F during the last 10 minutes of rising.
11 - Bake for 22–25 minutes until tops are golden brown and rolls are cooked through.
12 - Brush hot rolls immediately with melted butter. Sprinkle with parsley and Parmesan. Serve warm.