1Heat gas or charcoal grill. Cut bell peppers lengthwise into quarters; remove stems, seeds and membranes. Lightly brush onion slices with oil.
2Place pepper wedges, skin side down, and onions on grill over medium heat. Cover grill; cook about 10 minutes, turning occasionally, until pepper skins are completely blackened and blistered and onions are tender.
3Set onions aside. Immediately place pepper wedges in medium bowl. Cover bowl tightly with plastic wrap. Cool 5 minutes. Peel off blackened skin; rinse quickly with water. Cut peppers into strips. Return peppers to bowl; add onions.
4In small bowl, mix 1/4 cup oil, the vinegar, garlic, salt and pepper with whisk. Add 2 tablespoons dressing to onion mixture; toss to coat. In large bowl, toss arugula with remaining dressing. Top with onion mixture, walnuts and cheese. Serve immediately.