Bring a large pot of salted water to a boil and cook the pasta according to package directions, adding the broccoli florets to the water during the last 3-4 minutes of cooking.
While the pasta and broccoli cook, heat the olive oil in a large skillet or pan over medium heat.
Add the minced garlic and red pepper flakes to the skillet, sautéing for about 1 minute until fragrant but not browned.
Add the rinsed chickpeas to the skillet and cook for 3-5 minutes, allowing them to lightly toast and absorb the flavors.
Drain the pasta and broccoli, reserving about 1/4 cup of the pasta cooking water.
Add the pasta, broccoli, and vegetable broth to the skillet with the chickpeas.
Toss everything together over medium heat for 1-2 minutes until heated through, adding the reserved pasta water if the dish seems too dry.
Remove from heat and stir in the fresh lemon juice.
Season with salt and pepper to taste, and top with grated Parmesan cheese if desired before serving.