Wrap tofu blocks in several layers of heavy-duty paper towels. Press with a heavy object for about 30 minutes to remove excess water. Remove paper towels, pat tofu dry, and cut into 1-inch cubes; set aside.
With food processor running, drop garlic through food chute; process until minced. Add onion and parsley; pulse 3 times. Add chickpeas and tofu; pulse twice. Scrape down sides. Add egg and next 5 ingredients; pulse 4 times or just until beans are chopped (mixture should be chunky; do not over process). Shape mixture into 8 (3-inch) patties, using 1/3 cup for each patty.
Heat olive oil in a large nonstick skillet over medium heat. Add patties, and cook 5 minutes on each side or until browned. Serve immediately with Cucumber Mint Relish.