Combine warm milk, sugar, and yeast in a bowl and allow it to sit until foamy.
Add melted butter, egg, salt, and flour, then knead into a smooth dough and let it rise until doubled in size.
Mix melted butter, garlic, parsley, and salt to prepare the garlic butter.
Roll out the dough into a rectangle and brush evenly with the garlic butter.
Sprinkle mozzarella, cheddar, and Parmesan cheese evenly over the dough.
Roll the dough tightly, slice into equal rolls, and arrange them in a greased baking dish.
Let the rolls rise again, then bake until golden and fully cooked.
Brush with remaining garlic butter after baking and serve warm.
