01 - Combine warm milk, sugar, and yeast in a large bowl. Let sit for 5-10 minutes until foamy and activated.
02 - Whisk in melted butter, egg, and salt. Gradually incorporate flour until a soft, shaggy dough forms.
03 - Turn dough onto a floured surface and knead for 7-8 minutes until smooth, elastic, and no longer sticky.
04 - Place dough in a greased bowl, cover with plastic wrap or towel, and let rise in a warm, draft-free area until doubled in volume, approximately 1 hour.
05 - While dough rises, mix softened butter, minced garlic, mozzarella, Parmesan, parsley, and salt until well combined into a spreadable paste.
06 - Punch down risen dough and roll into a 12x16-inch rectangle. Spread filling evenly over entire surface, leaving a small border at edges.
07 - Starting from a long edge, roll dough tightly into a cylinder, pinching seam to seal.
08 - Cut log into 12 equal portions using a sharp knife or dental floss. Place rolls cut-side up in a greased 9x13-inch baking dish.
09 - Cover dish with towel and let rolls rise for 25-30 minutes until puffy and noticeably expanded. Preheat oven to 350°F during final 10 minutes.
10 - Bake for 22-25 minutes until tops are golden brown and centers are fully cooked through.
11 - Immediately brush hot rolls with melted butter, then sprinkle with fresh parsley and Parmesan. Serve warm for optimal flavor and texture.