Make the sauce: Place the first 5 ingredients in a blender, and process until smooth.
Make the patties: Place 1 cup onion and the next 7 ingredients (through 4 garlic cloves) in a food processor; process until smooth, scraping sides of bowl occasionally. Place the bean mixture in a large bowl; stir in ¼ cup of the breadcrumbs. Divide the bean mixture into 6 equal portions, shaping each into a ½-inch-thick patty. Place the remaining breadcrumbs in a shallow dish. Dredge the patties in the breadcrumbs.
Heat a large nonstick skillet over medium-high heat. Add 2 teaspoons of the oil to the pan; swirl to coat. Add 3 patties to the pan; cook 3 minutes on each side or until browned. Repeat procedure with the remaining oil and patties.
Warm the mini pitas according to package directions. Top each pita with ½ cup lettuce, ⅓ cup tomato, ⅓ cup cucumber, and 4 teaspoons onion. Drizzle each serving with about 3 tablespoons of the sauce; top with 1 patty.
Craving more veg-friendly recipes? Shop our collection of vegetarian and vegan cookbooks, including our new Vegan Thanksgiving and Vegan Christmas cookbooks!