Using a food processor, grind the oyster crackers, Ritz crackers, Parmigiano Reggiano cheese, 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 a quarter inch and heat over medium-high heat.
Pre-heat the oven to 200°F.
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 two 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.
Serve with lemon wedges alongside.