Using a food processor, grind the oyster crackers, Ritz crackers, parmigiano-reggiano, parsley, chives, thyme, Old Bay seasoning and garlic powder, if using. Transfer to a shallow bowl. Place the flour in another shallow bowl. In a third shallow bowl, beat the eggs and cream.
Fill a large skillet with enough EVOO to reach a depth of 1/4 inch and heat over medium-high heat. Preheat the oven to 200°. Season the fish fillets with salt and pepper. Coat the fish with the flour, shaking off any excess; coat with the egg mixture, then with the cracker crumbs. Working with 2 fillets at a time, fry the fish in the skillet, turning once, until deep golden, about 5 minutes. Transfer each batch to the oven to keep warm.