01 - Combine warm milk, sugar, and yeast in a large bowl. Let stand for 5-10 minutes until mixture becomes foamy.
02 - Stir melted butter, egg, and salt into yeast mixture. Gradually add flour, mixing until soft dough forms.
03 - Turn dough onto floured surface and knead for 7-8 minutes until smooth and elastic.
04 - Place dough in greased bowl, cover, and let rise in warm place until doubled in size, about 1 hour.
05 - Combine softened butter, minced garlic, mozzarella, Parmesan, parsley, and salt in a bowl during rising time.
06 - Punch down risen dough and roll out into 12x16-inch rectangle on floured surface.
07 - Spread cheese and garlic filling evenly over entire surface of dough.
08 - Starting from long edge, roll dough tightly into log shape.
09 - Slice log into 12 equal pieces. Place rolls cut-side up in greased 9x13-inch baking dish.
10 - Cover dish and let rolls rise for 25-30 minutes until puffy. Preheat oven to 350°F.
11 - Bake for 22-25 minutes until golden brown and completely cooked through.
12 - Brush hot rolls with melted butter. Sprinkle with parsley and Parmesan. Serve warm.