If you are using fresh broccoli, zap it first for 2 or 3 minutes in the microwave with a bit of water. If you are using frozen, thaw in advance or zap in the microwave for a minute or two to thaw it. Either way, drain, then set aside.
Peel and chop garlic; set aside.
Set a pot of salted water on to boil.
Heat oil in a skillet over medium heat. Add the garlic, and sauté for 1 minute. Add the broccoli, sauté until it is tender -- about 7 minutes. Stir in the drained chickpeas, lower the heat and cover to allow the chickpeas to warm through.
Meanwhile, if the water is boiling now, pop in the pasta and cook until tender to the bite. Drain the pasta. Return the pasta to the pot, add the broccoli mixture, and put the pasta pot over medium heat. Toss everything together, let it heat through for another minute or so, toss again, and serve.
Serve garnished on top if desired with a bit of olive oil and Parmesan, and with a wedge of lemon on the side if available.
Notes
You can use 1 medium bunch of fresh broccoli, chopped or 3 cups (20 oz / 600 g) of frozen chopped broccoli. 2 cups of cooked chickpeas = 1 15oz / 420g can, drained. Optional: you can add a handful of chopped fresh pepper or ½ teaspoon of red pepper flakes to the frying pan when you add the garlic.