Preheat broiler. Broil tomatoes and garlic on a foil-lined rimmed baking sheet 4 minutes.
Cook pasta according to package directions. Drain, reserving ⅓ cup pasta water.
Heat oil in a large skillet; sauté spinach 1 minute. Add reserved pasta water, cheese, and red pepper; cook until cheese melts. Add tomato mixture, pasta, olives, and salt; toss with basil before serving.