Place the quartered onion, garlic cloves, and parsley in a food processor and pulse until roughly chopped. If you do not have a processor, finely chop with a knife.
In a large bowl, combine the ground beef, ground lamb, and the squeezed bread. Add the chopped aromatics along with salt, pepper, allspice, cayenne, cardamom, cumin, sumac, nutmeg, and paprika. Mix well until the ingredients are evenly combined.
With wet hands, form the meat mixture into 10 logs. Wrap each log around a skewer, shaping them into an even layer about 1 inch thick.
Preheat your grill or grill pan to medium-high heat. Lightly oil the grates or pan. Place the skewered koftas on the grill and cook for about 4 minutes on one side.
Turn and cook for another 4 to 6 minutes until browned and cooked through. Remove from the grill and let rest for a few minutes before serving. Enjoy with pita bread, a side salad, or your favorite dipping sauce.