Preheat the oven to 425 degrees. Line two baking sheets with parchment paper.
In a large bowl, toss the cauliflower florets and chickpeas with the olive oil, cumin, smoked paprika, turmeric, cinnamon, garlic powder, salt, and black pepper until evenly coated.
Spread the mixture in a single layer across the two baking sheets. Roast for 25 to 30 minutes, stirring once halfway through, until the cauliflower edges are browned and the chickpeas are crisp.
While the vegetables roast, stir the tahini and lemon juice together in a small bowl to make a thin sauce. Add a tablespoon of water if needed to reach a drizzling consistency.
Arrange the roasted cauliflower and chickpeas on a large platter. Top with sliced cucumber, halved cherry tomatoes, and chopped parsley. Drizzle with the tahini sauce and serve with the warmed pita breads on the side.