If using wooden skewers, soak them in water for at least 30 minutes prior to grilling to prevent burning.
In a large mixing bowl, combine the ground lamb, parsley, half of the mint, 1 minced garlic clove, paprika, cumin, half of the salt, and black pepper. Mix gently by hand until just combined, being careful not to overwork the meat.
Divide the lamb mixture into 8 equal portions. Mold each portion tightly around a skewer to form a 4-inch oblong log shape.
Preheat the grill to medium-high heat. Lightly oil the grates with a high-smoke-point oil to prevent sticking.
Grill the kofta skewers for 8 to 10 minutes, turning occasionally, until nicely charred on all sides and cooked to an internal temperature of 160 degrees F.
While the lamb is cooking, prepare the yogurt sauce by whisking together the plain yogurt, lemon juice, remaining minced garlic, remaining mint, and remaining salt in a small bowl.
Remove the kofta from the grill and let them rest for 3 to 5 minutes. Serve warm alongside the garlic yogurt sauce.