Combine minced garlic, cumin, coriander, paprika, turmeric, cinnamon, cayenne pepper, olive oil, lemon juice, salt, and pepper in a large mixing bowl. Add chicken thighs and massage the marinade into the meat until evenly coated. Cover and refrigerate for at least 1 hour, preferably overnight.

While the chicken marinates, prepare the garlic sauce by whisking together Greek yogurt, minced garlic, lemon juice, tahini, and salt in a separate bowl until smooth. The sauce should have a pourable consistency. If it's too thick, add 1 to 2 teaspoons of water. Refrigerate until serving time.

Preheat your grill or stovetop skillet over medium-high heat. Remove chicken from the refrigerator and let it sit at room temperature for 10 minutes. Cook chicken for 6 to 7 minutes per side until you see dark brown grill marks with some blackened edges. Use a meat thermometer to confirm the internal temperature reaches 165°F.

Transfer cooked chicken to a cutting board and rest for 5 minutes. Slice into thin strips against the grain.

Warm your pita bread briefly on the grill or in a dry skillet for about 30 seconds per side until soft and pliable. Assemble by layering sliced chicken, fresh vegetables, and pickles on the pita, then drizzle generously with the creamy garlic sauce. Fold and serve immediately while everything is warm.