In a large bowl, combine the olive oil, plain yogurt, ground cumin, ground coriander, ground paprika, ground turmeric, ground cinnamon, ground allspice, black pepper, salt, minced garlic, lemon juice, and white vinegar.
Add the chicken or beef/lamb strips to the marinade and toss to coat evenly.
Cover the bowl and refrigerate for at least 1 hour, or preferably overnight for better flavor.
Preheat a grill, grill pan, or skillet over medium-high heat.
Remove the meat from the marinade and thread onto skewers (if using a grill) or place directly into the pan (if using a skillet).
Cook the meat for 5-7 minutes per side, or until fully cooked and slightly charred.
If using a grill pan or skillet, you may need to cook in batches to avoid overcrowding.
Warm the pita bread or flatbread in the oven or on a skillet.
Slice the cooked shawarma meat into thin strips.
Place the warm bread on a serving platter.
Top with shawarma meat, and add sliced tomatoes, cucumbers, and onions.
Garnish with fresh parsley.
Drizzle with shawarma sauce or tahini sauce if desired.
Enjoy your meal!