In a food processor, combine the garbanzo beans, 3 to 4 tablespoons flour, herbs, garlic, cumin, cayenne, egg, and salt and pepper; pulse together until almost smooth. Transfer mixture to bowl. The mixture should be firm enough to form balls; if not, add additional flour as needed. Shape mixture into balls about 2 inches in diameter. Toss in remaining 1/2 cup flour to coat all over. Set aside until oil is hot enough to fry.
Heat oil over medium-high heat until about 375 degrees F. Test with some extra falafel mix to see if the temperature is right; it should sink and rise to the surface and float. Add falafel balls in batches so as not to crowd them and cook until crisp and golden, about 8 minutes. Carefully remove from oil and drain on paper towels.
Fill pita halves with a few falafel balls, cucumber, lettuce, onions and peppers, and top with yogurt sauce.
Sesame Mint Yogurt Sauce:
Combine all ingredients in a bowl until well incorporated. Season with salt and pepper, to taste. Refrigerate until ready to serve.