In a large bowl, combine the yogurt, olive oil, minced garlic, cumin, paprika, turmeric, coriander, allspice, cinnamon, cayenne pepper (if using), lemon juice, salt, and black pepper.
Add the chicken or beef/lamb strips to the marinade. Mix well to coat the meat evenly. Cover and refrigerate for at least 2 hours, or overnight for best results.
Preheat your grill, skillet, or oven to medium-high heat.
If using a grill or skillet, cook the marinated meat for about 5-7 minutes per side, or until fully cooked and slightly charred. If using an oven, preheat to 400°F (200°C), place the meat on a baking sheet, and bake for about 20-25 minutes, or until cooked through and slightly crispy on the edges.
Once cooked, let the meat rest for a few minutes, then slice into thin strips.
Warm the pita bread or flatbreads. Place the cooked shawarma meat in the center of each bread.
Top with fresh vegetables, pickles, and drizzle with tahini sauce or garlic sauce if desired.
Enjoy your meal!