Combine Greek yogurt, chopped mint, minced garlic, lemon juice, and salt in a small bowl. Stir well, drizzle with olive oil, and refrigerate until needed.

Toss sliced red onion with red wine vinegar and a pinch of salt in a small bowl. Set aside at room temperature for at least 10 minutes - the onion will soften and turn pink.

Combine ground lamb, grated onion (squeezed dry), minced garlic, parsley, cumin, coriander, cinnamon, cayenne, smoked paprika, salt, and black pepper in a large bowl. Mix with your hands until just combined - do not overwork the meat.

Pinch off a small piece of the mixture and cook it briefly in a dry skillet. Taste and adjust salt or spice if needed.

Divide the mixture into 8 equal portions. Shape each portion into a log around a skewer, pressing firmly so it adheres. The kofta should be about 12 cm long and 3 cm wide.

Place shaped kofta on a baking sheet and refrigerate for 20 minutes. This firms the mixture and helps it hold on the grill.

Heat an outdoor grill or cast-iron grill pan over high heat. Brush the grates or pan surface with oil.

Place kofta on the grill and cook without moving for 3 to 4 minutes, until a dark crust forms underneath. Rotate and cook for another 3 to 4 minutes on the second side.

Turn once more and cook for 2 to 3 minutes until cooked through. An instant-read thermometer should read 70 C / 160 F at the center.

Transfer kofta to a plate and rest for 3 minutes.

Warm flatbread directly over a gas flame or in a dry skillet for 30 seconds per side until pliable and lightly charred.

Spread a generous spoonful of mint yogurt down the center of each flatbread. Layer shredded lettuce, sliced tomato, cucumber, and pickled red onion on top.

Slide 2 kofta off the skewers onto each wrap. Squeeze a lemon wedge over and fold the flatbread around the filling. Serve immediately.