Preheat oven to 425°F (220°C). Line a large baking sheet with parchment.
Toss cauliflower florets and chickpeas with olive oil, za'atar, salt, and cumin. Spread in a single layer on the baking sheet.
Roast for 30-35 minutes, stirring halfway, until cauliflower has golden edges and chickpeas are crispy.
While vegetables roast, whisk together yogurt, tahini, lemon juice, garlic, and water until smooth. Add more water if needed to reach drizzling consistency.
Spread tahini yogurt on a serving platter. Top with roasted cauliflower and chickpeas.
Scatter pomegranate seeds and parsley over everything. Serve warm or at room temperature.