Preheat the oven to 375 degrees F.
Put the fish in a large colander and rinse under cold running water. Pat dry with paper towels and transfer to a large non-reactive baking dish. Season both sides of the fish with 1 tablespoon of olive oil, and 1/2 teaspoon of the salt.
In a large bowl, combine the remaining 2 tablespoons of oil with the tomatoes, onions, wine, garlic, parsley, oregano, thyme, remaining 1/2 teaspoon of salt, and paprika. Arrange half of the tomato mixture under the fish, lay the fish on top, and arrange the remaining tomato mixture over the top.
Bake until the juices run clear and the onions are beginning to crisp and slightly blacken along the edges, about 40 minutes, basting occasionally with the pan juices.
Remove from the oven and let rest for 15 minutes. With 2 spoons, loosen the head from the body of the fish, lift away and discard. Run 1 of the spoons along the spine of the fish, and gently break the flesh into 2 fillets. Lift the fillets onto the serving platter. Carefully lift the spine and other bones out of the fish and discard. Place the remaining fish fillets on the platter and serve with the tomato topping.