In a large bowl, combine warm milk, yeast, and sugar. Let stand for 5 minutes until foamy.
Add melted butter, salt, and flour. Mix until a dough forms. Knead for 5-7 minutes until smooth and elastic.
Place the dough in a greased bowl, turning to coat. Cover and let rise in a warm place for 1 hour, or until doubled in size.
In a small bowl, combine softened butter, minced garlic, mozzarella cheese, and parsley.
Punch down the dough and roll it out into a large rectangle. Spread the garlic cheese mixture evenly over the dough.
Roll the dough up tightly and slice into 12 equal rolls. Place the rolls in a greased baking dish.
Cover and let rise for another 30 minutes.
Preheat oven to 375°F (190°C). Bake for 20-25 minutes, or until golden brown.