Set one oven rack in the upper third and another in the lower third, then preheat to 425°F. The upper position is for browning the vegetables; the lower position will warm the bread.
In a large mixing bowl, whisk the olive oil with cumin, paprika, salt, coriander, turmeric, black pepper, and cayenne, then toss in the cauliflower and onion before distributing them across a rimmed baking sheet. A uniform spice coating and a single layer give the vegetables even exposure to the heat.
Place the sheet on the upper rack and roast for 30 to 40 minutes, turning the vegetables once or twice and adding a drizzle of olive oil if they appear dry. Check for golden surfaces, lightly crisp edges, and tender stems before taking the pan out.
While the vegetables roast, combine the lemon juice, 1 teaspoon harissa, garlic, and salt in a small bowl and leave for 1 to 2 minutes. This brief lemon bath mellows the garlic before it joins the sesame paste.
Whisk the tahini into the garlic mixture, then incorporate ice water in 1-tablespoon additions. Stop when the sauce flows in a smooth ribbon, using less or more than the listed water as the tahini’s thickness requires.
Taste the sauce and adjust with additional harissa, lemon juice, or salt as desired. A creamy sesame flavor with lively acidity and balanced heat signals that it is ready.
During the final 5 minutes of vegetable roasting, warm the pita or flatbread on the lower rack, either directly on the rack or on another baking pan. The bread should feel warm and flexible for folding around the filling.
Finish the roasted cauliflower and onions with parsley and bring them to the table with the warmed bread, tahini, tomato, cucumber, and olives. The fresh toppings provide a cool, juicy contrast to the hot, aromatic vegetables.