To prepare sauce, combine the first 3 ingredients, stirring with a whisk until blended. Cover and chill until ready to serve.
To prepare falafel, bring 3/4 cup water to a boil in a small saucepan; add bulgur to pan. Remove from heat; cover and let stand 30 minutes or until tender. Drain and set aside.
Preheat oven to 425°.
Combine chickpeas and the next 9 ingredients (through garlic) in a food processor; pulse 10 times or until well blended and smooth (mixture will be wet). Spoon chickpea mixture into a large bowl; stir in bulgur.
Divide mixture into 12 equal portions (about 1/4 cup each); shape each portion into a 1/4-inch-thick patty. Place patties on a baking sheet coated with cooking spray. Bake at 425° for 10 minutes on each side or until browned. Spread about 2 1/2 tablespoons sauce onto each flatbread. Top each flatbread with 2 falafel patties, 2 tomato slices, and chopped cilantro, if desired.