Bring a large pot of salted water to a boil. Add the pasta and cook according to the package instructions. Drain and set aside.

Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper. Transfer the chickpeas and chopped broccoli to the baking sheet, then toss them with just 1/3 of the olive oil, along with some salt and pepper. Roast for 15-20 minutes, or until the broccoli is golden brown around the edges.

Heat the remaining olive oil in a large skillet over medium-low heat. Add the garlic and cook for about 1 minute, until fragrant.

Reduce the heat to low and add the cooked pasta to the skillet, stirring to coat. Add the roasted broccoli and chickpeas, then drizzle with lemon juice. Season with salt and pepper to taste, and toss to combine. Top with parmesan and serve.