Generously salt a large pot of water and bring to a boil. Add the pasta and cook according to package directions, though you want to pull the pasta out when it is still slightly undercooked, or al dente.
While the pasta is cooking, bring a second pot of salted water the boil, and add the rapini. Cook it until wilted and the stems are tender, about 3-4 minutes. Pull from the boiling water and place immediately in ice water to stop the cooking process.
In a large frying pan or dutch oven, heat about 1/4 cup of olive oil over medium-high heat. Once the oil shimmers, add some salt and the roughly chopped garlic, and stir until fragrant. Add pepper flakes to taste.
Next, add in the beans, having drained them (and save the aquafaba!!). Stir well and toss and coat with the oil. Allow them to cook down until they start to pop open and release the starches.
Next add the cooked and drained rapini, and stir well.
Drain the pasta, but be sure to save some of the pasta water on the side. Add the pasta to the sauce and toss well, adding additional olive oil or pasta water if needed to make a proper sauce.
Finish with a grating of lemon zest, a squeeze of lemon, and a garnish of grated parmesan cheese.