In a large mixing bowl, combine the ground lamb, minced garlic, grated onion, finely chopped fresh mint, coriander, ground cumin, ground ginger, sea salt, black pepper, and cayenne pepper. Use your hands to mix everything until well combined. Be careful not to overwork the meat, as this can lead to a tough texture.
Once the mixture is thoroughly combined, divide it into equal portions. Shape each portion into an oval or cylindrical shape, about 2-3 inches in length. If you’re using skewers, press the kofta around the skewer firmly to ensure they hold their shape during cooking.
In a separate bowl, mix together the Greek yogurt, chopped fresh mint, freshly squeezed lemon juice, ground cumin, minced garlic, cayenne pepper, sea salt, and minced cucumber. Stir until all the ingredients are well incorporated. Taste and adjust the seasoning as needed. Set aside to allow the flavors to meld.
Preheat your grill or oven to medium-high heat. If grilling, place the kofta skewers directly on the grill grates and cook for about 4-5 minutes on each side, or until they are browned and cooked through. If baking, place the kofta on a baking sheet and bake for about 20 minutes, flipping halfway through.
Once cooked, remove the kofta from the grill or oven and let them rest for a few minutes. Serve the Lamb Kofta warm with the yogurt sauce drizzled on top or on the side for dipping. You can also accompany them with warm pita bread, fresh salad, or your favorite grain for a complete meal.