Heat grill. In large bowl, combine oil, peppered seasoned salt and basil; mix well. Add vegetables; toss to coat.
When ready to grill, place onion and bell peppers in grill basket or directly on gas grill over medium-low heat or on charcoal grill 4 to 6 inches from medium coals. Cook 6 minutes.
Add mushrooms to grill basket; cook 6 to 10 minutes or until vegetables are crisp-tender, turning occasionally.