In a bowl, mix flour, cornmeal, sugar, baking powder, salt, and paprika. In another bowl, beat eggs to blend with buttermilk and 1/4 cup butter. Stir peppers into egg mixture mixture. Pour liquids into flour mixture and stir just until evenly moistened.
Scrape batter into a buttered 8-inch square pan and spread smooth.
Bake in a 400° oven until bread springs back when lightly pressed in the center and begins to pull from pan sides, about 30 minutes (25 minutes in a convection oven).
Cut bread into squares. Lift from pan with a slender spatula. Serve hot or cool.