Step 1

In a medium bowl, whisk together the olive oil and lemon juice. Whisk in the garlic, cumin, paprika, curry powder, turmeric, cinnamon, pepper flakes, salt, and black pepper to taste.

Step 2

Pour the marinade into a zip-top plastic bag and add the chicken, massaging it to coat evenly. Refrigerate for at least 1 hour or up to overnight.

Step 3

In a small bowl, combine 3 tablespoons water, the tahini, olive oil, garlic, lemon juice, and salt. The consistency should be smooth enough to pour; add more water to loosen if needed.

Step 4

Arrange the lettuce, cucumbers, tomato, and olives on a platter.

Step 5

Preheat a grill pan over medium-high heat (or preheat a grill to medium-high). Spray the pan with oil (or rub the grates with oil). Grill the chicken until cooked through, 5 to 6 minutes per side. Transfer to the open half of the platter and tent with foil.

Step 6

Wipe the grill pan clean and spray it with more oil (or just rub the grates with oil again). Grill the onion wedges until they have grill marks, about 3 minutes per side. Grill the pitas until heated through, about 1 minute per side. Cut the pitas in half and transfer them to the platter. Garnish the tahini sauce with the parsley. Serve with the lemon wedges.