In a medium saucepan, heat oil over medium. Add garlic and red-pepper flakes, and cook until fragrant, about 30 seconds (do not brown). Add chickpeas, season with salt, and cook 5 minutes. Add tomatoes and broth, and bring to a boil. Reduce to a simmer, and cook until sauce has reduced slightly, 20 minutes. Add basil, and cook 5 minutes more. Remove basil.
While sauce is cooking, cook pasta in a large pot of boiling salted water until al dente; drain pasta, and return to pot.
Add sauce to pasta, and toss. Serve with Parmesan, and garnish with torn basil.