In a large bowl, combine 2 ¼ cup flour, sugar, salt & yeast; add ½ cup butter or margarine. With mixer at low speed, gradually pour 2 cups hot tap water (120-130F) into dry ingredients. Add egg and increase speed to medium; beat 2 minutes, scrap9ing bowl occasionally with rubber spatula. Beat in ¾ cup flour or enough to make a thick batter; continue beating 2 minutes more, scraping bowl. With a spoon, stir in enough additional flour (about 2 ½ cups) to make a soft dough. Turn dough onto lightly floured surface & knead until smooth and elastic, about 10 minutes. Shape dough into ball & place in greased large bowl; grease top & cover with towel. Let rise in a warm place (80-85 degrees) away from draft until doubled – about 1 ½ hours.
Punch down by pushing the center of dough with fist; then pushing edges into center. (Can be refrigerated at this time by covering rightly with plastic wrap).
To shape into rolls, cut dough into 30 equal pieces & shape into balls and place into a greased pan. Cover with towel; let rise in warm place until doubled (1/2 – 1 hour). Preheat oven to 425 degrees. Bake rolls for 15-20 minutes, or until golden brown. Brush rolls with melted butter. Remove from pans immediately.