Pat the boneless skinless chicken thighs dry with paper towels.
In a large bowl, combine the olive oil, lemon juice, minced garlic cloves, ground cumin, ground coriander, smoked paprika, turmeric, cinnamon, salt, and black pepper.
Add the chicken thighs to the bowl, ensuring each piece is fully coated in the marinade.
Cover the bowl and refrigerate for at least 4 hours, or preferably overnight (up to 24 hours) for the best flavor.
Preheat your grill to medium-high heat. If using a cast iron skillet, heat it over medium-high heat with a tablespoon of olive oil until shimmering.
Remove the chicken from the marinade, letting any excess drip off. Discard the remaining marinade.
Place the chicken thighs on the hot grill or skillet. Cook for 6-8 minutes per side, or until the chicken is cooked through and has nice char marks. The internal temperature should reach 165°F (74°C).
Once cooked, transfer the chicken to a cutting board.
Tent it loosely with foil and let it rest for 5-10 minutes. This allows the juices to redistribute, keeping the chicken tender.
After resting, slice the chicken thighs thinly against the grain into strips.
In a small bowl, combine the Greek yogurt, mayonnaise, minced garlic cloves, lemon juice, and salt.
Stir everything together until well combined and smooth.
Taste and adjust seasoning if necessary. If you prefer a thinner sauce, you can add a tiny splash of water or more lemon juice.
Warm the pita bread slightly, either on the grill, in a dry skillet, or in the microwave, until soft and pliable.
Lay a warm pita bread on a clean surface.
Spread a generous amount of the creamy garlic sauce down the center of the pita.
Arrange a layer of shredded lettuce, sliced tomato, sliced cucumber, and sliced red onion over the sauce.
Pile a good portion of the thinly sliced chicken shawarma on top of the vegetables.
Sprinkle with fresh chopped parsley.
Carefully roll up the pita tightly, tucking in the sides as you go to create a secure wrap. Serve immediately.