Heat oven to 425 degrees F. Grease 9 by 9-inch pan.
Whisk together the dry ingredients in a large bowl.
Whisk together the eggs, both whole and buttermilk, and peppers in a smaller bowl, add to dry ingredients, and stir just until moistened. Fold in the melted butter.
Pour the batter into the greased pan and spread evenly. Bake on the middle oven rack for 25 to 30 minutes, until lightly browned and a knife or toothpick inserted in the center comes out clean.