In a large bowl, dissolve yeast and sugar in warm milk. Let sit 5–10 minutes until foamy.
Add melted butter, salt, and egg (if using). Mix well.
Gradually add flour and knead until a soft, elastic dough forms.
Place dough in a greased bowl, cover, and let rise until doubled (about 1 hour).
Mix softened butter, garlic, parsley, and salt for the filling.
Roll dough into a rectangle. Spread garlic butter evenly over the surface.
Roll tightly into a log and slice into 12 rolls.
Arrange in a greased baking dish. Cover and let rise 30 minutes.
Bake at 375°F (190°C) for 22–25 minutes until golden.
Brush with melted butter and serve warm.