01 - Combine warm milk, sugar, and yeast in a large bowl. Let stand for 5–10 minutes until mixture becomes foamy, indicating the yeast is active.
02 - Add melted butter, egg, and salt to the yeast mixture. Gradually incorporate flour until a soft, sticky dough forms.
03 - Turn dough onto a lightly floured surface. Knead for 7–8 minutes until smooth and elastic, adding minimal flour only if necessary to prevent sticking.
04 - Place dough in a greased bowl, turning once to coat. Cover with plastic wrap or a clean towel and let rise in a warm, draft-free area until doubled in bulk, approximately 1 hour.
05 - While dough rises, combine softened butter, minced garlic, mozzarella, Parmesan, parsley, and salt in a medium bowl until evenly distributed.
06 - Punch down risen dough to release air. Roll out on a lightly floured surface into a 12x16-inch rectangle, approximately 1/4-inch thick.
07 - Spread cheese mixture evenly over the dough, leaving a 1/2-inch border around the edges.
08 - Starting from a long edge, roll dough tightly into a log, pressing gently to seal the seam.
09 - Cut log into 12 equal pieces using a sharp knife or dental floss. Place rolls cut-side up in a greased 9x13-inch baking dish, spacing evenly.
10 - Cover dish with a towel and let rolls rise for 25–30 minutes until puffy and nearly doubled. Preheat oven to 350°F during the final 15 minutes of rising.
11 - Bake for 22–25 minutes until golden brown on top and cooked through. Internal temperature should reach 190°F when tested with a thermometer.
12 - Immediately brush hot rolls with melted butter. Sprinkle with chopped parsley and additional Parmesan cheese. Serve warm while cheese is still melty.