In a bowl, mix flour, cornmeal, 1/3 cup sugar, the baking powder, and the salt. In another bowl, beat eggs to blend with buttermilk and 1/4 cup butter. Stir in chiles and cheese. Pour egg mixture into flour mixture and stir just until evenly moistened.
Scrape batter into a buttered 8- or 9-inch square pan; spread level. In a bowl, mix remaining 1 tablespoon sugar and the chili powder. Sprinkle evenly over batter.
Bake in a 400° oven until bread springs back when lightly pressed in the center and begins to pull from pan sides, 20 to 25 minutes.
Cut into pieces. Serve hot or at room temperature.