Place cauliflower and brussels sprouts on an oven tray; drizzle with half the oil. Season; toss to coat. Place chickpeas on another oven tray; sprinkle with paprika, cumin and coriander. Season; drizzle with remaining oil.
Roast vegetables and chickpeas for 25 minutes. Add cavolo nero to vegetables; roast a further 5 minutes or until vegetables are tender and chickpeas are crisp.
Meanwhile, make tahini dressing. Combine ingredients in a small bowl.
Serve vegetables and chickpeas drizzled with dressing.