Prepare the grill for direct heat (if using a grill pan, see Notes). If using a gas grill, set it to 450 degrees. If using a charcoal grill, fill a chimney starter with charcoal, light it, and when the coals are white-gray with ash, pour them onto the charcoal grate, adding more charcoal, if necessary. Put the lid on the grill, making sure the vents are open all the way. When all of the coals are gray and hot, about 15 minutes, your grill should be medium-hot. (Use a grill thermometer, or test the heat by holding your hand, palm-down, about 4 inches from the grate, making sure that nothing flammable, such as clothing, is near the heat. If you can hold it there for about 4 seconds, the heat should be at medium, or about 450 degrees. Pull your hand away from the heat before it gets painful.)

While the grill is preheating, in a large bowl, stir together the onion, zucchini and parsley until combined. Add the turkey, 1 teaspoon of the za'atar, the cardamom, ¼ teaspoon of the salt and ¼ teaspoon of the cumin, and gently mix until well combined.

Dampen your hands with water, then use them to divide the mixture into 8 equal portions, shaping each to form a 2 ½- to 3-inch oblong kebab. Thread two onto each skewer, spacing the kebabs about 1 inch apart and pressing to secure them in place. Grease each kebab with a little nonstick cooking spray or olive oil (to help prevent sticking), then sprinkle with the remaining 1 teaspoon of za’atar.

Grill the kebabs for 10 to 12 minutes, turning them a few times for even browning/grill marks, or until the interior temperature registers 165 degrees on an instant-read thermometer.

Meanwhile, in a medium bowl, whisk together the yogurt, tahini, oil, the remaining ¼ teaspoon each of salt and cumin, and the cayenne pepper. Add the lemon juice and whisk to combine. Taste, and add more tahini and/or lemon juice, as needed.

Serve warm, with pitas on the side and the tahini sauce for dipping.