To prepare sauce, combine the first 5 ingredients in a blender, and process until smooth.
To prepare patties, combine 1 cup onion and next 7 ingredients (through 4 garlic cloves) in a food processor, and process until smooth, scraping sides of bowl occasionally. Place bean mixture in a large bowl; stir in 1/4 cup breadcrumbs. Divide bean mixture into 6 equal portions, shaping each into a 1/2-inch-thick patty. Place remaining 1/4 cup breadcrumbs in a shallow dish. Dredge patties in breadcrumbs.
Heat 2 teaspoons oil in a large nonstick skillet over medium-high heat. Add 3 patties to pan; cook 3 minutes on each side or until browned. Repeat procedure with remaining 2 teaspoons oil and patties.
Warm mini pitas according to package directions. Place 1 pita on each of 6 plates. Top each serving with 1/2 cup lettuce, 1/3 cup tomato, 1/3 cup cucumber, and 4 teaspoons onion. Drizzle each serving with about 3 tablespoons sauce; top each serving with 1 patty.
Wine note: Light in body and tannin, pinot noir is the perfect red wine for robust vegetarian dishes. These burgers include spices like coriander and cumin, which are echoed in Kim Crawford Marlborough Pinot Noir ($15), with its savory nuances and aromas of smoke and dried herbs. Bright fruit and ample acidity help to cut the burgers' rich tahini sauce. -Jeffery Lindenmuth