In a large mixing bowl, combine the plain yogurt, olive oil, lemon juice, minced garlic, ground cumin, ground coriander, ground paprika, ground turmeric, ground cinnamon, ground black pepper, and salt. Mix well.
Add the thinly sliced chicken thighs or lamb to the marinade, ensuring all the pieces are well coated. Cover and refrigerate for at least 2 hours, preferably overnight.
Preheat your grill or a large skillet over medium-high heat.
Cook the marinated meat in batches, turning occasionally, until the meat is fully cooked and slightly charred, about 6-8 minutes per side. If using a skillet, you may need to add a little oil to prevent sticking.
In a small bowl, whisk together the tahini, lemon juice, minced garlic, and water. Add more water as needed to reach a smooth, pourable consistency. Season with salt to taste.
Warm the pita bread or flatbreads on the grill or in a skillet.
Spread a generous amount of the tahini sauce on each pita bread.
Add the cooked meat slices on top.
Garnish with sliced tomatoes, cucumbers, red onions, chopped parsley, and pickles if using.
Roll or fold the pita bread around the fillings to create a wrap.
Enjoy your meal!