Bring a pot of salted water to a boil, cook pasta about 80%, about 8 minutes.
In a saute pan, cook garlic cloves and broccoli florets on medium heat. Once florets are tender, add chickpeas, pasta and a few scoops of pasta water. Saute all together.
Once water has evaporated and pasta is al dente and well integrated, sprinkle parmiginao reggiano cheese. Toss quickly and serve.