In a mixing bowl, combine olive oil, Greek yogurt, shawarma spice blend, lemon juice, and minced garlic. Add the chicken thighs and coat well. Marinate for at least 30 minutes, or up to overnight in the refrigerator.

Preheat the grill to medium-high heat. Remove chicken from marinade and grill for 6-7 minutes per side, or until the internal temperature reaches 165°F (75°C).

In a small bowl, whisk together tahini, water, lemon juice, minced garlic, and salt until smooth. Adjust the consistency with more water if needed.

In serving bowls, layer chopped romaine, diced cucumber, cherry tomatoes, red onion, and parsley. Slice the grilled chicken and place on top. Drizzle with tahini sauce before serving.