Preheat the oven to 425 degrees. Line a baking sheet with parchment paper.
In a large bowl, toss the cauliflower florets and chickpeas with 2 tablespoons olive oil, cumin, smoked paprika, turmeric, salt, and black pepper until evenly coated.
Spread the mixture in a single layer on the prepared baking sheet. Roast for 25 to 30 minutes, stirring once halfway, until the cauliflower is tender and the chickpeas are slightly crisp.
While the vegetables roast, whisk together the tahini, lemon juice, minced garlic, remaining 1 tablespoon olive oil, and enough water to reach a pourable consistency.
Transfer the roasted cauliflower and chickpeas to a serving bowl. Drizzle with the tahini dressing and toss gently to coat.
Sprinkle the chopped parsley and mint over the top just before serving.