Preheat oven broiler. Grease a broiling pan or line pan with aluminum foil.
In a small bowl, mix the Parmesan cheese, butter, mayonnaise, and lemon juice. Season with dried basil, pepper, onion powder, and celery salt. Mix well and set aside.
Arrange fillets in a single layer on the prepared pan. Broil a few inches from the heat for 2 to 3 minutes. Flip fillets and broil a couple more minutes. Remove fillets from oven and cover with Parmesan cheese mixture on the top side. Broil for two more minutes or until the topping is brown and fish flakes easily with fork.