Combine first 5 ingredients in a small bowl; cover and chill.
Combine bulgur, boiling water, and lemon juice in a bowl; stir well. Let stand 30 minutes or until liquid is absorbed.
Heat 2 teaspoons oil in a large non-stick skillet over medium heat. Add green onions and the next 6 ingredients (green onions through garlic); sauté 1 minute or until green onions are tender. Remove from heat; stir in parsley.
Place chickpeas in a food processor; process until ground. Add chickpeas and green onion mixture to bulgur mixture; toss well. Add flour and egg whites; stir well. Divide mixture into 6 equal portions, shaping into 3-inch patties.
Heat 2 teaspoons oil in skillet coated with cooking spray. Place over medium heat until hot. Add patties; cook 3 minutes on each side or until browned. Place patties on bottom halves of buns; dress with parsley sprigs, if desired. Top each with 1/4 cup cucumber sauce and top half of bun.