Falafel Sandwiches with Sesame Mint Yogurt Sauce

• 2 (15-ounce) cans garbanzo beans (chickpeas), drained and rinsed
• 3 to 4 tablespoons, plus 1/2 cup all-purpose flour
• 1/4 cup packed fresh cilantro leaves
• 1/2 cup packed fresh parsley leaves
• 2 cloves garlic
• 1 teaspoon ground cumin
• 1/8 teaspoon cayenne pepper
• 1 large egg, lightly beaten with a fork
• Salt and pepper
• 3 quarts vegetable oil, for frying
• 3 good quality pita breads, cut in 1/2
• Sesame Mint Yogurt Sauce, recipe follows

Fixings:

• 1 English cucumber, peeled and chopped into 1-inch pieces
• 1 small head iceberg lettuce, chopped into bite-sized pieces
• 1 small red onion, thinly sliced
• 1 green pepper, seeded and chopped into bite-sized pieces

Sesame Mint Yogurt Sauce:

• 2 cups plain whole-milk yogurt, preferably Greek-style
• 1 bunch mint leaves, finely chopped
• 1/4 to 1/2 teaspoon dark sesame oil
• 1 lemon, zested and juiced
• Salt and pepper