Make the Shawarma Marinade: In a large mixing bowl, combine the olive oil, fresh lemon juice, minced garlic, ground cumin, ground coriander, smoked paprika, ground cardamom, ground turmeric, ground cinnamon, cayenne pepper, kosher salt, black pepper, and Greek yogurt (if using). Whisk everything together thoroughly until the marinade is smooth and all spices are fully incorporated.
Marinate the Chicken: Pat the chicken thighs dry with paper towels. Add them to the bowl with the marinade and toss thoroughly until every piece is completely and evenly coated. Cover the bowl tightly with plastic wrap or transfer to a large zip-lock bag. Refrigerate for a minimum of 1 hour, preferably 4 to 8 hours or overnight up to 24 hours. Remove from fridge 20-30 minutes before cooking.
Cook the Chicken (Skillet Method): Heat a large cast iron skillet or heavy-bottomed pan over medium-high heat until very hot, about 2-3 minutes. Add 1 tablespoon of olive oil and swirl to coat. Add the marinated chicken thighs to the skillet in a single layer without crowding. Cook for 5-6 minutes on the first side until a deep golden-brown crust forms, then flip and cook for another 4-5 minutes until the internal temperature reaches 165°F (74°C).
Slice the Chicken: Transfer the cooked chicken to a cutting board and rest for 5 minutes. Using a sharp chef's knife, slice the rested chicken against the grain into thin, diagonal strips. For extra crispy edges, return the sliced chicken to the hot pan with any accumulated juices and toss for 1-2 minutes over high heat.
Prepare the Toppings and Sauce: While the chicken rests, slice the tomatoes and cucumbers into thin rounds or half-moons. Roughly chop the fresh parsley. Prepare your garlic sauce (toum) or tahini sauce. Warm the pita bread in a dry skillet for 30 seconds per side or wrap in foil and heat in a 350°F (175°C) oven for 5 minutes.
Assemble and Serve: Spread a generous layer of garlic sauce or tahini sauce along the center of the warmed pita bread. Pile on the sliced chicken shawarma, then top with sliced tomatoes, cucumbers, pickled vegetables, and fresh parsley. Fold or roll the pita around the filling and serve immediately. For a bowl, serve the sliced chicken over fluffy rice or a bed of greens, then add toppings and drizzle generously with sauce.