In a large mixing bowl, whisk together the plain yogurt, extra virgin olive oil, and fresh lemon juice until smooth. Add the minced garlic, cumin, coriander, paprika, turmeric, cinnamon, allspice, cardamom, black pepper, kosher salt, and sumac.
Whisk everything together until you have a thick, evenly colored paste with no dry spice pockets remaining. Pat the chicken thighs dry with paper towels, then add them directly to the bowl with the marinade.
Use your hands or tongs to fully coat every piece, making sure the marinade gets into any folds in the meat. Cover the bowl tightly and refrigerate for at least 2 hours, though 8 to 24 hours will give you the deepest flavor.
Remove the chicken from the fridge about 15 minutes before cooking so it is not ice cold going into the pan. Heat your cast iron grill pan or heavy skillet over medium-high heat until it is very hot but not smoking.
Shake off any excess marinade from each piece of chicken, then lay it in the pan without overcrowding, working in batches if needed. Cook for 5 to 6 minutes per side, resisting the urge to move the chicken too soon so it can develop a good crust.
Use your meat thermometer to confirm the internal temperature has reached 165 degrees Fahrenheit at the thickest part. Transfer the cooked chicken to a cutting board and tent it loosely with foil.
Let it rest for 5 minutes so the juices redistribute back through the meat instead of running out when you cut it. Slice the chicken into thin strips against the grain for that classic shawarma texture.
While the chicken rests, warm your pita bread in a dry skillet or directly over a gas flame for a few seconds per side. Spread garlic sauce or hummus on the warm pita, then layer in the sliced chicken.
Top with your favorite fresh vegetables and a final sprinkle of sumac before rolling or folding to serve.