In a mixing bowl, combine warm milk, sugar, and yeast. Let it sit for 5 minutes until frothy.
Add softened butter, salt, and beaten egg to the yeast mixture. Mix well.
Gradually add flour, one cup at a time, mixing until a soft dough forms.
Knead the dough on a floured surface for about 10 minutes until smooth and elastic.
Place the dough in a greased bowl, cover, and let it rise in a warm place for 1 hour or until doubled in size.
Preheat oven to 375°F (190°C). Punch down the dough and divide it into 12 equal pieces. Shape each piece into a ball and place on a greased baking sheet.
Cover and let the rolls rise for another 30 minutes.
Bake in the preheated oven for 12-15 minutes or until golden brown.
Brush the hot rolls with melted butter and serve warm.