Bring a large pot of salted water to a boil. Cook the pasta according to the package directions, adding the broccoli florets in the last few minutes of cooking to keep them tender yet crisp.
While the pasta and broccoli are cooking, heat olive oil in a skillet over medium heat. Add the minced garlic and red pepper flakes, cooking briefly until fragrant but not browned.
Stir in the rinsed chickpeas and cook them in the skillet for several minutes, allowing them to toast a bit and soak up the fantastic flavors from the garlic and oil.
Once the pasta and broccoli are tender, drain them but reserve a small amount of pasta water. Add the pasta and broccoli to the skillet with the chickpeas, along with vegetable broth.
Gently toss everything together over medium heat for a couple of minutes until heated through. If it seems dry, splash in a bit of the reserved pasta water.
Remove from heat and stir in the fresh lemon juice. This adds a nice brightness to the dish.
Add salt and pepper to taste. If you'd like, top with grated Parmesan cheese before serving.