Cook the Pasta: Fill a large pot with heavily salted water and bring it to a boil. Add the fusilli and cook until it’s slightly underdone, just shy of al dente. Reserve some of the pasta water, then drain the pasta thoroughly.
Prepare the Chickpea Base: Place the chickpeas in a large bowl and lightly mash them using a fork or potato masher. Aim for a texture where the chickpeas are about half-crushed.
Cook the Aromatics: In a large skillet, heat the olive oil over medium heat. Add the smashed garlic cloves and cook until golden brown, which should take about 2 minutes. Stir in the diced onion, rosemary, chili flakes, and a pinch of salt. Let the mixture cook, stirring occasionally, until the onion softens, approximately 10 minutes.
Build the Sauce: Add the mashed chickpeas to the skillet, along with the chickpea cooking liquid or water. Allow the mixture to come to a simmer and cook gently for about 5 minutes, or until much of the liquid has reduced.
Combine Pasta and Sauce: Add the drained pasta and parsley to the skillet, stirring to coat the pasta thoroughly with the sauce. Let it cook for 1-2 minutes until the pasta finishes cooking and absorbs some of the sauce.
Finish with Flavor: Mix in the grated cheese, butter, and lemon zest, stirring to combine. Taste and season with additional salt, black pepper, and chili flakes if desired.
Serve and Garnish: Transfer the pasta to serving dishes, drizzle with extra olive oil, and sprinkle with additional Parmigiano-Reggiano for garnish. Serve immediately.