01 - In a large mixing bowl, whisk together yogurt, olive oil, lemon juice, minced garlic, cumin, coriander, smoked paprika, turmeric, cinnamon, cayenne pepper, salt, and black pepper until combined. Add chicken thighs and coat thoroughly. Cover and refrigerate for at least 1 hour, or overnight for optimal flavor.
02 - In a food processor, blend garlic cloves and salt until finely minced. With the machine running, slowly drizzle in neutral oil in a thin stream, alternating with lemon juice, until a smooth, fluffy emulsion forms. Add ice water as needed for creaminess, then season to taste.
03 - Preheat a grill, grill pan, or skillet over medium-high heat. Remove chicken from marinade, letting excess drip off. Grill or sear chicken for 5 to 7 minutes per side until deeply charred and fully cooked through. Allow to rest 5 minutes; then slice into strips.
04 - Arrange warm pita or flatbread on plates. Pile sliced chicken over bread, top with generous garlic sauce, sliced tomato, cucumber, red onion, and a sprinkle of fresh herbs. Serve immediately.