1. Heat broiler. Line a large baking sheet with foil. Coat foil with nonstick cooking spray. Coat a 10- inch nonstick skillet with nonstick cooking spray. Add onion and cook over medium heat, 2 minutes. Add mushrooms and continue to cook for 4 minutes. Add soy sauce; cook 1 minute. Remove from heat.
2. Heat rice in microwave following package directions, 90 seconds. Transfer rice and skillet contents to a food processor. Add chickpeas. Cover and pulse until mixture resembles ground beef (the chickpeas should be chopped up). Transfer to a large bowl.
3. Add shredded zucchini, cheese and bread crumbs to bowl with rice mixture. Stir to combine. Stir in egg, salt and pepper until all ingredients are moistened. Let mixture rest 5 minutes.
4. With wet hands, shape mixture into six 3-1/2-inch patties, a scant cup for each. Place on foil-lined pan. Broil, 3 inches from heat, for 8 minutes. Carefully flip over and continue to broil an additional 8 minutes, until browned and crispy. Serve with green salad alongside.