Heat dry skillets in upper and lower thirds of oven while preheating oven to 450°F.
Whisk together cornmeal, flour, baking powder and soda, and salt.
Add eggs, buttermilk, and 1 cup melted butter, then quickly stir together.
Remove hot skillets from oven. Divide remaining 1/2 cup melted butter between them, then divide batter between pans.
Bake in upper and lower thirds of oven, switching position of pans halfway through baking, until golden and a tester inserted in center comes out clean, 15 to 20 minutes total.
• If you are making corn bread ahead for croutons, reheat remainder in skillets or wrapped in foil, in a 350°F oven 10 to 15 minutes before serving.