Prepare the Marinade: In a large bowl, combine the yogurt, olive oil, lemon juice, garlic, tomato paste, salt, baharat, black pepper, oregano, cayenne pepper, paprika, and sumac. Mix thoroughly.
Marinate the Chicken: Incorporate the diced chicken into the marinade, making sure every piece is thoroughly coated. Seal the bowl with a lid or plastic wrap and let it chill in the refrigerator for a minimum of 2 hours, ideally overnight, to enable the flavors to meld beautifully.
Prepare the Skewers: Preheat your grill to medium-high heat. Thread the marinated chicken pieces onto the soaked wooden skewers, leaving a small gap between each piece for even cooking.
Grill the Chicken: Place the skewers on the grill, turning occasionally, until the chicken is fully cooked and slightly charred on the outside—about 12-15 minutes. Make sure the internal temperature of the chicken reaches 165°F (75°C).
Make the Yogurt Sauce: While the chicken is grilling, prepare the yogurt sauce. In a small bowl, mix together the yogurt, cucumber (if using), garlic, lemon juice, cayenne, mint, and salt. Mix thoroughly until everything is evenly blended, then place it in the refrigerator until you're ready to enjoy.
Serve: After grilling the chicken, take it off the heat and allow it to sit for a few minutes to retain its juices. Serve the Shish Taouk hot, alongside the yogurt sauce, with warm pita bread, rice, or salad.