1. Preheat oven to 500º.
2. Combine bread crumbs, cornmeal, salt and cayenne in a large sealable plastic bag and shake to mix.
3. Season fish with salt and pepper on both sides.
4. Put each piece of fish in crumbs, shake and remove.
5. Dip one fish piece in egg, shake off excess and then return to crumb mixture and shake until it is well coated then remove to a plate. Repeat with second piece of fish.
6. Heat 3 tablespoons of oil in a heavy ovenproof skillet over high heat until hot but not smoking.
7. Fry fish until undersides are golden brown, about 1 minute.
8. Turn over, add remaining tablespoon of oil and cook 1 minute more.
9. Put skillet in upper third of oven and bake until fish is just cooked through, about 5 minutes.
Accompaniment: lemon wedges and tartar sauce.
Serve with Roasted Fries.