Preheat the oven to 400°F (200°C). Line a large baking sheet with parchment paper.
Thoroughly dry the rinsed chickpeas with a clean kitchen towel. In a large bowl, toss the cauliflower florets and chickpeas with the olive oil, smoked paprika, cumin, salt, and black pepper.
Spread the seasoned cauliflower and chickpeas in a single, even layer on the prepared baking sheet. Roast for 25 to 30 minutes, tossing halfway through, until the cauliflower is deeply golden and tender, and the chickpeas are crispy.
While the vegetables roast, prepare the dressing. In a small bowl, whisk together the tahini, lemon juice, minced garlic, and a pinch of salt. The mixture may seize initially; gradually whisk in warm water, one tablespoon at a time, until the sauce becomes smooth and drizzle-friendly.
Transfer the hot roasted cauliflower and chickpeas to a serving platter. Drizzle generously with the creamy tahini sauce and garnish with freshly chopped parsley.