In a large bowl, combine the ground beef, grated onion, minced garlic, parsley, cumin, coriander, paprika, salt, black pepper, and cayenne pepper (if using). Mix until well combined.
Divide the mixture into 8 equal portions and shape each portion into an elongated oval or sausage shape.
Preheat a grill or grill pan over medium-high heat. Brush the grill with olive oil to prevent sticking.
Place the kofta on the grill and cook for about 4-5 minutes on each side, or until browned and cooked through.
While the kofta is grilling, prepare the garlic yogurt sauce by combining the Greek yogurt, minced garlic, lemon juice, salt, and mint (if using) in a small bowl. Mix well and set aside.
Serve the kofta hot with the garlic yogurt sauce on the side. Enjoy with pita bread or over a bed of rice.