In 4- to 6-quart slow cooker stir together undrained tomatoes, tomato paste, onion, garlic, chopped olives, snipped parsley, capers, anchovy paste, basil, cayenne pepper, 1/4 teaspoon salt, and 1/4 teaspoon ground black pepper.
Cover and cook on low-heat setting 8 to 10 hours or high-heat setting for 4 to 5 hours.
Remove half of sauce (about 5-1/2 cups). Set aside for additional meals.
If using low-heat setting, turn to high-heat setting. Add shrimp and halved olives to sauce in cooker. Cover and cook 5 minutes more or until heated through. Serve over hot cooked pasta or rice. Sprinkle with shaved Parmesan cheese. Makes 6 servings plus 5-1/2 cups.