Combine Greek yogurt, olive oil, and lemon juice in a large mixing bowl. Whisk vigorously until smooth and emulsified.

Add minced garlic, cumin, coriander, cardamom, smoked paprika, turmeric, cinnamon, cayenne pepper, salt, and black pepper to the yogurt mixture. Mix thoroughly until the marinade appears uniform in color.

Pat chicken thighs completely dry with paper towels. Cut chicken into bite-sized strips or leave whole depending on serving preference. Add to marinade and coat thoroughly. Cover and refrigerate for minimum 3 hours but preferably overnight.

For the garlic sauce: Remove any green sprouts from garlic cloves. Add peeled garlic and salt to a food processor. Process for 1-2 minutes until finely minced.

With the food processor running, drizzle one tablespoon of oil very slowly. Stop and scrape down sides after each oil addition. Alternate between oil and lemon juice additions in small amounts.

Continue alternating oil and lemon juice in small amounts until all oil is incorporated. Add ice water at the end. Finished sauce should be bright white, fluffy, and hold stiff peaks. If sauce breaks, start fresh with new garlic paste and slowly incorporate the broken sauce.

Heat a large cast iron skillet or grill pan over high heat until very hot. Remove chicken from marinade, letting excess drip off. Place chicken in hot skillet and do not move for the first 3-4 minutes to develop char. Cook in batches if necessary to avoid crowding.

Flip chicken pieces and continue cooking until internal temperature reaches 165°F on an instant-read thermometer. Look for deeply charred edges. Let chicken rest for 5 minutes after cooking, then slice against the grain if serving in wraps.

Warm pita bread briefly. Spread generous amount of garlic sauce on bread. Layer with chicken, vegetables, and additional garlic sauce. Serve immediately.