Preheat the oven or grill (grill is preferred and the smoke gives a great taste to the fish) to 475°.
Lightly oil a large rimmed baking sheet. Lay the redfish fillets, skin side down, on the baking sheet and brush them with 2 tablespoons of the olive oil. Sprinkle with Old Bay seasoning.
Roast or grill (cover the grill after putting the fillets on it) the redfish fillets on the bottom rack of the oven for about 20 minutes, or until the flesh flakes with a fork. Depending on size the cook time will vary.
Meanwhile, in a small bowl, mix the parsley and garlic and melted butter. Transfer the fish to a platter, drizzle with the parsley-garlic butter and serve with lemon wedges.
The fillet will peel off of the fish having been protected by the skin and scales.