Preheat your oven to 425°F (220°C). Lay the rinsed chickpeas on a clean kitchen towel and gently roll them around to strip off all surface moisture.
Place the cauliflower florets and dried chickpeas onto a large baking sheet. Drizzle with extra-virgin olive oil, then sprinkle with the ground cumin and half of the kosher salt. Toss well to coat evenly, then spread into a single, uncrowded layer.
Roast in the oven for 20 to 25 minutes, tossing halfway through, until the cauliflower florets are deeply browned at the edges and the chickpeas are crisp.
While the tray roasts, make the sauce. In a small bowl, whisk together the tahini, lemon juice, grated garlic, and remaining salt. The mixture will thicken into a tight, clumpy paste.
Whisk in warm water one tablespoon at a time. Continue whisking until the paste loosens into a smooth, creamy, pourable dressing.
Transfer the warm cauliflower and chickpeas to a wide serving bowl. Drizzle generously with the tahini dressing, scatter the fresh parsley over top, and toss lightly to coat before serving.