01 - Combine yogurt, olive oil, garlic, cumin, coriander, paprika, sumac, cinnamon, salt, pepper, and lemon juice in a large bowl. Add sliced meat and toss to coat thoroughly. Cover and refrigerate for at least 1 hour, preferably overnight for optimal flavor penetration.
02 - Preheat oven to 430°F or prepare grill to medium-high heat. Ensure cooking surface is properly heated before proceeding.
03 - Thread marinated meat slices tightly onto skewers. Place on baking tray or grill and cook for 35-45 minutes, turning occasionally until meat is thoroughly browned and cooked through. Alternatively, sear in batches in a hot skillet until well-browned.
04 - Whisk together Greek yogurt, mayonnaise, minced garlic, lemon juice, salt, and pepper in a small bowl until smooth and homogeneous. Refrigerate until ready to serve.
05 - Place pita breads or flatbreads in the warm oven for 2-3 minutes until pliable and heated through.
06 - Slice cooked meat thinly across the grain. Spread garlic sauce generously over warmed bread. Layer with meat, lettuce, tomato, cucumber, onion, and parsley. Roll or fold bread securely and serve immediately while warm.