1. Rinse quinoa thoroughly in a fine sieve; drain. Bring 2 cups water to a boil in a medium saucepan. Add quinoa; return to a boil. Stir quinoa; cover, and reduce heat. Simmer until quinoa is tender but still chewy, about 15 minutes. Fluff quinoa with a fork; let cool.

2. Meanwhile, process garlic, tahini, lemon juice, and 1/4 cup cold water in a food processor until smooth. If necessary, thin with water until pourable. Transfer dressing to a small bowl; cover. Refrigerate until ready to use.

3. Put turkey, spices, mint, scallions, and salt in a clean bowl of the food processor; pulse until a smooth paste forms. Add quinoa; process until mixture clumps around the blade, about 2 minutes. Transfer to a bowl. With dampened hands, roll about 2 tablespoons quinoa mixture into a ball; flatten slightly, and set aside on a plate. Repeat with remaining mixture to make 24 patties total.

4. Heat a dry large cast-iron skillet or grill pan over medium heat until hot. Working in batches, lightly coat both sides of patties with cooking spray. Cook patties in skillet, turning once, until cooked through, about 8 minutes per side. Transfer patties to a clean plate, and loosely cover with foil to keep warm.

5. Divide lettuce, cucumber, and red onion among pita breads; top each with 4 quinoa patties. Drizzle each sandwich with 1 tablespoon plus 1 teaspoon tahini dressing, and fold pitas over filling.