In a bowl, mix together flour, sugar, salt, and yeast.
Add warm milk, softened butter, minced garlic, and the egg. Stir until a dough forms.
Knead the dough on a floured surface for about 8-10 minutes until smooth and elastic.
Place the dough in a greased bowl, cover, and let rise in a warm place for 1 hour or until doubled in size.
Preheat oven to 375°F (190°C).
Punch down the dough, divide into 12 pieces, and shape each piece into a roll.
Place the rolls in a greased baking dish, cover, and let rise for another 15 minutes.
Bake the rolls in the preheated oven for 15-20 minutes or until golden brown.
Brush with melted butter and sprinkle with chopped fresh parsley before serving.