Prepare the marinade: In a large bowl, whisk together 3 tablespoons olive oil, 3 tablespoons lemon juice, ¼ cup plain Greek yogurt, 4 grated or minced garlic cloves, 2 teaspoons cumin, 2 teaspoons paprika, 1½ teaspoons coriander, 1 teaspoon turmeric, 1 teaspoon fine sea salt, ½ teaspoon black pepper, ½ teaspoon cardamom, ½ teaspoon cinnamon, ¼ teaspoon cayenne pepper, and ¼ teaspoon ground cloves.
Marinate the chicken: Pat the chicken thighs dry with paper towels. Add them to the marinade and turn until thoroughly coated on all sides. Cover and refrigerate for at least 2 hours or up to 12 hours.
Prepare the oven: Preheat the oven to 425°F and line a large rimmed baking sheet with aluminum foil.
Arrange the chicken: Remove the chicken thighs from the marinade, allowing the excess to drip back into the bowl while leaving a thin coating on the chicken. Arrange the thighs in a single layer on the prepared baking sheet, leaving a little space between each piece. Discard any marinade remaining in the bowl.
Bake: Bake for 22-27 minutes, beginning to check the chicken after 22 minutes. Continue baking until the thickest part of the chicken registers approximately 160°F on an instant-read thermometer.
Broil: Switch the oven to high broil. Broil the chicken for 1-3 minutes, watching it closely, until the surface is deeply browned in spots and the thickest part reaches at least 165°F. The total oven time will usually be 25-30 minutes.
Rest and slice: Remove the chicken from the oven and let it rest for 5 minutes. Slice the thighs across the grain into strips.
Serve: Serve the chicken shawarma with lemon wedges. To make wraps, add the sliced chicken to warm pita or flatbread with tomato, romaine lettuce, red onion, and tzatziki.