In a mixing bowl, combine the Greek yogurt, grated cucumber, lemon juice, minced garlic, chopped mint, and salt. Stir until well-mixed, then cover and refrigerate for at least 30 minutes.

In a large bowl, add ground beef and ground lamb if using. Grate the onion directly in, then add minced garlic, chopped parsley, chopped mint, cumin, allspice, cinnamon, salt, and pepper. Mix gently until just combined.

With lightly oiled hands, take small portions of the mixture and shape them into oval or round meatballs, aiming for 1 to 1.5 inches in diameter. Arrange on a lined baking tray.

For pan-frying, heat olive oil in a skillet over medium heat and cook meatballs for 2-3 minutes on each side. For baking, preheat oven to 400°F (200°C) and bake for 18-20 minutes, flipping halfway. For grilling, thread onto skewers and grill for 3-4 minutes per side.

Once cooked, let the meatballs rest. Serve warm alongside the chilled cucumber mint sauce.