Make the marinade. In a large bowl, combine the olive oil, dried mint, crushed chile flakes, thyme, Aleppo pepper, tomato paste, Turkish sweet red pepper paste, black pepper, and salt. Whisk to blend.
Marinate the chicken. Add the chicken pieces to the bowl with the marinade. Cover and let sit at room temperature for at least 30 minutes or, ideally, refrigerate overnight and then allow the chicken to come to room temperature before grilling
Prepare the grill. Heat the rear element only of a gas grill to medium-high (about 400°F), creating both a hot direct-heat zone for searing and a cooler zone for more gentle cooking if needed.
Assemble the skewers. Remove the chicken from the marinade and thread the pieces onto skewers, leaving a small amount of space between each piece to encourage even cooking and browning.
Grill the chicken. Place the skewers over the hottest part of the grill and cook, turning every 3 to 4 minutes, until the chicken is lightly charred on all sides and cooked through, about 12 minutes total. If the outside is browning too quickly, move the skewers to the cooler side of the grill to finish cooking more gently. The chicken is ready when it reaches an internal temperature of 165°F.
Rest and serve. Transfer the skewers to a serving platter and let them rest for 3 to 5 minutes. Serve hot with tzatziki and steamed rice.
Notes
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Don’t have Turkish red pepper paste? Replace it with an additional tablespoon of tomato paste. Or, if you have roasted red peppers on hand, blend a small amount into the tomato paste to help bridge the gap.
No grill? Cook the skewers on a grill pan set over medium-high heat or roast them on a sheet pan in a 425°F oven until cooked through and lightly caramelized at the edges.