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 ready for meat.
03 - Thread marinated meat slices onto skewers, pressing tightly together. Place on baking tray or grill and cook for 35-45 minutes, turning occasionally until meat is browned and cooked through. Alternatively, sear in batches in a hot skillet until well-browned and cooked through.
04 - Mix Greek yogurt, mayonnaise, minced garlic, lemon juice, salt, and pepper in a small bowl until smooth and well combined. Refrigerate until ready to serve.
05 - Place pita breads or flatbreads in warm oven for 2-3 minutes until pliable and heated through.
06 - Slice cooked meat thinly against the grain. Spread sauce generously over warmed bread, layer with meat, lettuce, tomato, cucumber, onion, and parsley. Roll or fold securely and serve immediately while warm.