Heat the oven to 425°F. Rinse the chicken and pat it dry with paper towels. Cut away any excess fat and tuck the wings behind each breast.
Put the butter in a shallow baking pan (a 9x13-inch Pyrex pan or large oval baking dish works well). Put the pan into the oven while it's heating. When the butter is melted (about 10 minutes), remove the pan and set it on a heatproof surface or on a couple of potholders.
In a shallow, medium bowl, combine the Parmesan, flour, salt, herbes de Provence, paprika, cayenne, and lots of freshly ground pepper. Dredge a piece of chicken, skin side down, in the melted butter first and then in the cheese mixture. Use your hands, pressing gently, to coat evenly. Turn the chicken skin side up and push it to the side of the pan. Repeat with the remaining chicken pieces.
Bake, basting with the pan juices occasionally (tilt the pan and spoon the juices from the corners), until the chicken is well browned and cooked through, 50 to 60 minutes. (see a tip on basting baked chicken).