In a large ziplock bag, combine all marinade ingredients: minced garlic, ground coriander, cumin, cardamom, cayenne pepper, smoked paprika, salt, black pepper, lemon juice, and olive oil. Shake well to mix.
Add chicken thigh fillets to the ziplock bag. Seal the bag, push out excess air, and massage from the outside to coat every piece thoroughly with marinade.
Refrigerate for at least 3 hours, preferably overnight for best results.
While chicken marinates, make the yogurt sauce: Combine Greek yogurt, crushed garlic, cumin, lemon juice, salt, and pepper in a bowl. Mix well and refrigerate for at least 20 minutes to let flavors meld.
When ready to cook, remove chicken from fridge and let sit at room temperature for 10 minutes.
Heat a large non-stick skillet over medium-high heat. Add about 1 tablespoon of oil.
Place chicken pieces in the hot skillet in a single layer (cook in batches if needed to avoid overcrowding). Cook undisturbed for 4-5 minutes until beautifully browned and caramelized.
Flip each piece and cook for another 3-4 minutes until cooked through and golden brown.
Remove chicken from heat and let rest for 3-5 minutes, covered loosely with foil. Slice into strips if desired.
To serve: Warm flatbreads, spread with yogurt sauce, add lettuce, tomatoes, red onion, and shawarma chicken. Roll tightly and enjoy!