Heat the oven to 400F and line a large baking sheet with parchment paper. The hot oven helps the vegetables roast instead of soften, and the parchment makes the pan easier to clean.
Cut the broccoli into medium florets, remove the kale stems and chop the leaves, then scrub and slice the sweet potato into ¼” wide rounds. Keeping the sweet potato slices fairly even helps them finish roasting in the same window.
Toss the broccoli with oil, garlic, salt, and black pepper, rubbing the seasoning over the tops of the florets before arranging them down the center of the baking sheet. The broccoli should look lightly coated rather than drenched, which helps the edges brown instead of steam.
In the same bowl, stir together the chickpeas, oil, sriracha, and soy sauce, then spread them on one side of the sheet pan beside the broccoli. Give the chickpeas some space so they roast with a sizzle and develop firmer edges.
Use the same bowl again to mix the oil, curry powder, salt, and sriracha, then add the sweet potato slices and toss to coat before laying them on the remaining third of the pan. The slices should sit in a single layer so they can caramelize and turn tender in the center.
Roast for 10 minutes, then turn the broccoli and sweet potatoes and stir the chickpeas before returning the pan to the oven for 8 to 12 minutes more. The vegetables are ready when the broccoli is browned at the edges, the sweet potatoes are tender, and the chickpeas look slightly dried and roasted.