In a bowl, combine the olive oil, chicken, paprika, cumin, cardamom, turmeric, cinnamon, cayenne, lemon, garlic, and a large pinch each of salt and pepper. Let marinate for 15 minutes at room temperature or up to overnight in the refrigerator.Preheat the oven to 425° F. Arrange the chicken on a baking sheet. Bake 15 minutes, toss and bake another 5-10 minutes, or until cooked through. Switch the oven to broil. Broil 1-2 minutes, until the chicken chars on the edge. *Watch closely!Meanwhile, make the tahini. Combine all ingredients and 1/4 cup water in a blender and blend until smooth. If needed, add water to thin the sauce as desired. Season to taste with salt.To assemble, stuff/spread each pita with tahini, then lettuce, and cucumber. Add the chicken, red onion, avocado, and parsley. Drizzle over more tahini and harissa (recipe in notes).