Put the butter, sugar, and salt in a large bowl. In a small saucepan, heat the milk until warm; pour it over the butter mixture and let cool. In a small bowl, sprinkle the yeast over the warm water; set aside to proof until foamy, about 5 minutes.
Stir the yeast mixture into the butter mixture. Beat in the egg, then beat in the flour until you have a soft dough. Cover and refrigerate for at least 1 to 2 hours.
Two hours before baking, turn the dough out onto a floured surface and divide it in half. Divide each half into 6 equal portions, then divide each portion into 3 pieces. Roll each piece into a ball, dip into the melted butter, and place in a muffin tin, 3 balls to a muffin cup. Cover with plastic wrap and let rise in a warm place until doubled in bulk, about 1 1/2 hours.
Preheat the oven to 350 degrees F. Bake the rolls for 15-20 minutes, or until golden brown.