In a standing mixing bowl with dough hook, dissolve yeast in warm water. Let sit until lightly foamy, then stir in sugar and add egg, salt, warm milk, and 4 ounces of butter. Slowly add 5 cups flour, adding more as needed to make an elastic dough. Mix well, then roll out to floured surface and knead dough for about 5 minutes.
Place dough in buttered bowl, cover with towel, and set in a warm place to rise until double in bulk, about 1 hour.
Lightly oil the muffin pan. Punch down dough and form dough into 1-inch balls. Place 3 balls in each muffin tin. Fill muffin pan, cover with towel, and allow to rise an additional 1/2 hour.
Preheat oven to 425 degrees F.
Brush with remaining melted butter. Bake in preheated oven for 10 to 15 minutes, until golden brown.