Heat broiler. On a broiler-safe rimmed baking sheet, toss cherry tomatoes with chickpeas with one tablespoon olive oil; season with coarse salt and ground pepper. Broil, tossing occasionally, until tomatoes are slightly charred, 15 to 20 minutes.
Meanwhile, in a large bowl, whisk together remaining 3 tablespoons olive oil and white-wine vinegar; season with salt and pepper.
Add baby spinach, hot vegetables, and black olives. Toss with vinaigrette (spinach will wilt slightly).