Heat the oven to 220 C / 425 F with racks in the upper and lower thirds. Pat the chickpeas dry with a clean towel, rubbing off any loose skins, and cut the cauliflower into 4 cm / 1.5 inch florets.
Stir the cumin, smoked paprika, coriander, turmeric, cayenne, 1 tsp salt, and pepper together in a small bowl. Toss the chickpeas with 1 tbsp of the olive oil and half the spice mix on one 33 x 46 cm / 13 x 18 inch sheet pan. Toss the cauliflower with the remaining 2 tbsp oil and spice mix on a second pan of the same size, and spread both in a single layer.
Roast for 30 minutes, swapping the pans between racks and stirring at the 15-minute mark. The cauliflower is done when the edges are deeply browned and a knife slides into the stems easily. The chickpeas are done when the edges look dry and they rattle as you shake the pan.
While the pans roast, combine the quinoa, water, and 1/4 tsp salt in a 2-quart / 1.9 L saucepan and bring to a boil. Cover, reduce to low, and simmer for 15 minutes until the water is absorbed. Leave it covered off the heat for 5 minutes, then fluff with a fork.
Whisk the tahini, lemon juice, grated garlic, and 1/4 tsp salt in a small bowl, then add the cold water a tablespoon at a time until the sauce pours like heavy cream. Toss the sliced onion with the vinegar. Dice the cucumber, halve the tomatoes, and chop the parsley.
Divide the quinoa among 4 bowls and top with the cauliflower, chickpeas, cucumber, tomatoes, and onion. Drizzle with the tahini sauce, scatter the parsley over the top, and serve right away.