In a mixing bowl, combine yeast, sugar and milk; beat until smooth. Add butter, egg and salt; mix well. Add 3 cups flour; beat until smooth. Add enough remaining flour to form a soft dough. Knead on floured surface until smooth and elastic, about 6-8 minutes. Place in greased bowl, turning once to grease top. Cover and let rise in warm place until doubled, about 1 hour.
Punch the dough down and divide in half. Divide each half into 36 pieces and shape into balls. Place three balls each in greased muffin cups. Cover and let rise in warm place until doubled, about 30 minutes. Brush with butter. Bake at 375 °F for 15 to 18 minutes or until lightly browned. Remove to wire racks. Serve warm.