Preheat the oven to 400°F. Wash the cabbages and slice them into wedges, keeping a portion of the core on each slice so the cabbage holds together in one piece. Place each wedge on a parchment-lined baking sheet. Drizzle each wedge with olive oil.
In a medium bowl, mix the za’atar seasoning with the shredded Parmesan cheese and stir to combine. Top each cabbage wedge generously with this mixture and roast for 25-30 minutes, until the edges are crispy.
While the cabbage wedges are roasting, whisk together all the tahini yogurt sauce ingredients in a small bowl and set aside. Serve the cabbage warm with the tahini yogurt sauce drizzled over top.