Thaw fish, if frozen. For stuffing, in a mixing bowl stir together the onion, green sweet pepper, vinegar, basil, salt, cumin, and pepper. Add Parmesan cheese; mix well.
Rinse fish and pat dry with paper towels. Brush the outsides and cavities of fish with oil. Spoon one-fourth of the stuffing mixture into each fish cavity.
Brush a wire grill basket with cooking oil. Place fish in basket. Grill fish on an uncovered grill directly over medium-hot coals for 7 to 11 minutes or until fish flakes easily with a fork, turning once.
If desired, serve with new potatoes and garnish with basil sprigs. Makes 4 servings.