In a large bowl, combine the flour, cornmeal, sugar, yeast and salt. In a small saucepan, heat water and 2 tablespoons butter to 120°-130°. Add to dry ingredients; beat until moistened. Add egg; beat on medium speed for 3 minutes.
Turn onto a floured surface; knead until smooth and elastic, 6-8 minutes. Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about 1 hour.
Punch dough down. Turn onto a lightly floured surface; divide into 18 pieces. Shape each piece into a ball. Place in a greased 13x9-in. baking pan or two 9-in. round baking pans. Cover and let rise in a warm place until doubled, about 30 minutes.
Bake at 400° for 15-20 minutes or until golden brown. Melt remaining butter; brush over rolls. Invert onto wire racks.