Place racks in the middle and top positions of the oven; preheat to 425° F.
Arrange 2 lb. heirloom or other large tomatoes, cored, cut into 1½"-thick wedges, on a rimmed baking sheet. Drizzle with extra-virgin olive oil and season generously with kosher salt and freshly ground pepper; toss to coat. Roast in the middle of the oven until tomatoes slightly collapse and are somewhat dried, 25–30 minutes. Remove from the oven.
Heat the broiler.
In a medium bowl, combine the rinsed and drained chickpeas, cumin, smoked paprika, and Kosher or flake salt. Drizzle lightly with oil and toss to coat.
Spoon chickpea mixture over and around tomatoes.
Break 1 lb. feta into large pieces, cut into ½" thick slabs, and tuck around the tomatoes. Broil on the top rack until the tomatoes and feta are slightly blistered, 3-5 minutes.
Remove from oven and let sit for a few minutes.
Arrange the arugula and the torn, pitted green olives over the tomato-chickpea mixture. Drizzle some sherry vinegar or red wine vinegar and more oil over the mixture; season with pepper.
Serve as a side dish in a bowl or with pita wedges.