Add the onion, garlic, and parsley to a mini food processor and process until finely chopped. Alternatively, grate the onion and finely chop the garlic and parsley with a knife.

Transfer the mixture to a large bowl and add the ground beef, cumin, coriander, allspice (or cinnamon), salt, and pepper. Mix until combined.

Divide the mixture into 8 roughly even balls. Mold each ball around the pointed end of a skewer, making an oval kebab that comes to a point just covering the tip of the skewer.

If using wooden skewers, soak them in water for 15 minutes before threading the meat onto them.

Heat a grill pan over medium-high heat or prepare a grill. Brush the pan lightly with olive oil.

Grill the kebabs, turning occasionally, until brown all over and cooked through, about 10 minutes.

Transfer to a serving platter and serve with tzatziki sauce, flat bread, and sliced vegetables.

Mix all of the tzatziki sauce ingredients together in a bowl.

Refrigerate until ready to serve.