Preheat oven to 425° F.
In a shallow, medium bowl, mix Parmesan cheese, flour, and seasonings.
Rinse the chicken quarters; pat dry with paper towels.
Put half a stick of butter (4 tablespoons) in a shallow baking dish, preferably9 x 13-inch Pyrex pan and allow butter to melt in pan while oven is preheating. Takes just a few minutes. Remove pan when butter is melted, set on a heatproof surface, or a couple of potholders; allow oven to continue to preheat.
Dredge a piece of chicken in the melted butter, then in the cheese-flour mixture. Press gently to coat evenly. Turn the chicken skin side up and push it tothe side of the pan. Repeat with the remaining chicken pieces.
Bake about 50 to 60 minutes, drizzling with some lightly seasoned olive oil about halfway through the baking time. The chicken will be well browned and cooked through.