Mix 2¼ cups flour, sugar, salt, yeast and ½ cup butter with mixer at low speed.
Add 2 cups hot water (100-110ºF).
Add egg, increase speed to medium for 2 minutes, scraping the sides of the bowl.
Beat in ¾ cup flour or enough to make thick batter.
Beat 2 minutes scraping sides.
Stir in 2½ cups flour to make soft dough.
Turn out onto lightly floured surface.
Knead until smooth (10minutes).
Shape into a ball. Place in a large greased bowl, turn dough to cover with oil.
Cover bowl with a towel. Let rise until doubled in size (1hour).
Punch down, press edges into center, knead slightly.
Shape into ball cover with bowl to rest for 15 minutes.
Melt ½ cup butter in 17¼ x 11½ pan.
On lightly floured surface, using a floured rolling pin, roll dough ½" thick.
Cut with 2½" biscuit cutter.
Dip into melted butter, fold in half, and place on baking sheet.
Cover with towel. Let rise 40 minutes.
Preheat oven to 425º F.
Bake rolls 18-20minutes.