Sauté the shrimp and fish in olive oil in a medium saucepan or Dutch oven 3 to 5 minutes or until cooked through; remove from pan, and set aside. Place onion and garlic in pan. Cook, stirring constantly, 3 to 5 minutes or until tender. Add anchovies, and stir until dissolved. Add rice, and stir until well-coated and translucent, about 1 to 2 minutes.
Add wine, and simmer until absorbed. Stir in the hot broth, 1 cup at a time, stirring frequently, until each addition has been absorbed. (The entire process should take 20 to 25 minutes.) Stir in tomato paste with the last addition of broth.
Stir in reserved seafood, fresh basil, and cheese.