Cook garlic and red pepper flakes in oil in a 12-inch heavy skillet over moderate heat, stirring, until garlic is golden, about 1 minute. Add broccoli and salt and cook, breaking up frozen chunks and stirring occasionally, until broccoli is thawed and crisp-tender, 5 to 7 minutes. Stir in chickpeas and cook until heated through.
Cook pasta in a 6- to 8-quart pot of boiling salted water until al dente. Reserve 1/2 cup pasta cooking water, then drain pasta in a colander. Add pasta and reserved cooking water to broccoli and chickpeas in skillet and cook over moderate heat, tossing, until combined well. Serve drizzled with additional olive oil.
