In a small bowl, mix warm milk, sugar, and yeast. Let sit for 5–10 minutes until foamy.
In a large mixing bowl, combine flour and salt. Add yeast mixture, softened butter, and egg. Stir until a dough forms.
Knead dough on a floured surface for 8–10 minutes (or use a stand mixer with a dough hook for 5–6 minutes) until smooth and elastic.
Place dough in a greased bowl, cover, and let rise in a warm place for 1 hour or until doubled in size.
Punch down dough and divide into 12 equal portions. Shape each into a ball and place in a greased 9x13-inch baking dish.
Cover and let rise for 30–40 minutes, until puffy.
Preheat oven to 375°F. Bake rolls for 15–18 minutes, until golden brown on top.
While baking, combine melted butter, minced garlic, parsley, and salt.
Brush garlic butter over hot rolls as soon as they come out of the oven. Serve warm.