In a food processor, combine the rinsed garbanzo beans, shredded carrot, flour, bread crumbs, parsley, 1 tablespoon (15 ml / 0.5 fl oz) of the olive oil, halved garlic, coriander, salt, cumin, and black pepper.
Cover and pulse until the mixture is finely chopped and holds together when pressed. Be careful not to over-process; you want some visible texture from the beans and carrots.
Shape the mixture into four 3-inch patties, each about 1/2 inch thick. Gently brush both sides of the patties with the remaining 1 tablespoon (15 ml / 0.5 fl oz) of olive oil.
Wrap the pita bread rounds in aluminum foil to warm on the grill later.
To prepare the Cucumber Yogurt Sauce, combine the yogurt, shredded cucumber, tahini, minced garlic, and salt in a small bowl.
Stir until well-blended.
Cover and chill in the refrigerator for at least 20 minutes to allow the flavors to meld.
Preheat your grill to medium heat. For a charcoal grill, arrange coals for direct heat. For a gas grill, preheat and then reduce heat to medium.
Place the patties on the greased grill rack directly over the heat.
Grill for 10 to 12 minutes, uncovered, flipping once halfway through, until the patties are golden brown and heated through.
Place the foil-wrapped pitas on the grill for the last few minutes of cooking to warm them up.
To assemble, spread a generous layer of the chilled Cucumber Yogurt Sauce inside each warm pita.
Top with shredded romaine lettuce, a grilled falafel patty, and a sprinkle of diced tomato, if desired.
Serve immediately and enjoy!
Don't over-process the falafel mixture; a little texture from the chickpeas and carrots is key to a great patty.
