Rinse wings and pat dry.
With your hands, force each joint open until it snaps, then cut wings apart at joints.
Cut through the midsection of each wing (the part with 2 bones) and through the joints.
You can cook wing tips, or reserve them for other uses, such as broth.
On a sheet of waxed paper, mix cornmeal, paprika, marjoram, and pepper.
In shallow pan, beat egg and water to blend.
Coat wing pieces in egg, then coat with cornmeal mixture (pat on lightly for extra-thick crust).
Lay pieces slightly apart in an oiled 10- by 15-inch baking pan.
Bake pieces in a 400° oven for 15 minutes, then drizzle evenly with melted butter.
Continue baking until thickest part of meat at bone on the largest piece is no longer pink (cut to test), about 25 minutes longer.