1/4 cup fresh mint leaves, finely chopped, plus more for serving
4 naan flatbreads, pita, or burger buns
1 medium cucumber, thinly sliced lengthwise into ribbons
Fresh cilantro leaves and tender stems, for serving
Thinly sliced red onion, sliced tomato, and green lettuce, for serving, if desired
Cut the chicken thighs into chunks, discarding any excess fat. Grind with a meat grinder or mince finely in a food processor, then transfer to a large bowl.
Mince 4 of the garlic cloves and add them to the chicken. Add cumin, paprika, coriander, turmeric, cayenne, ginger, and 2 tablespoons of the yogurt. Squeeze in the juice of half the lemon, being careful not to let seeds in. Stir well. Cover with plastic and refrigerate for at least 1 hour and up to 6 hours.
Meanwhile, mince the remaining 1 clove garlic and add it to a bowl with the remaining 1/4 cup plus 2 tablespoons yogurt and juice from the remaining half lemon. Stir in the jalapeño and mint and season with salt. Set aside or keep refrigerated.
Light one chimney full of charcoal. When all the charcoal is lit and covered with gray ash, pour out and spread the coals evenly over half of coal grate. Alternatively, set half the burners of a gas grill to high heat. Set cooking grate in place, cover grill and allow to preheat for 5 minutes. Clean and oil the grilling grate.
While the grill preheats, divide and shape the chicken mixture into 4 patties (or 6 if you’d like smaller patties). Season the patties generously all over with salt, then place directly over hot side of grill. Cook for 6 minutes on each side, or until the center reads 165°F (74°C) on an instant-read thermometer.
Toast the naan or burger buns on the grill. Then fill the naan or burger buns with sliced cucumber, lettuce, if using, and the chicken patties. Spoon the yogurt sauce on the patties, then sprinkle with fresh mint leaves and cilantro. Top with tomato and onion, if using, and serve.