1. Bring water to a boil in a small pot. Add bulgur and simmer, partially covered, over medium heat 8 minutes, or until liquid is absorbed. Turn off heat, cover pot and let bulgur rest 5 minutes.
2. Pulse garlic in a food processor until minced; set aside 1/2 teaspoon. Add chickpeas to remaining garlic and puree. Transfer mixture to a medium bowl and add carrot, scallions, cumin, cayenne pepper and 1/2 teaspoon salt. Fluff bulgur with a fork and stir into chickpea mixture.
3. Shape 3/4 cup chickpea mixture into a 3/4-inch-thick patty; repeat with remaining chickpea mixture.
4. Heat oil in a medium nonstick skillet over medium-high heat. Add patties and cook 3 minutes on each side, or until browned.
5. In a small bowl, whisk together yogurt with reserved garlic and pinch of salt. Split pitas open and fill each with 1 patty, 2 slices tomato, 2 slices cucumber and 2 tablespoons yogurt sauce.