In a large pot of boiling salted water, cook broccoli until tender and bright green, about 4 minutes. With a slotted spoon, transfer broccoli to a food processor. Return water to a boil and cook pasta according to package instructions. Reserve 2 cups pasta water; drain pasta and return to pot.
To food processor, add oil, Parmesan, lemon zest and juice, parsley, and garlic. Puree until smooth, about 2 minutes, scraping down side as needed. Transfer pesto to pot with pasta. Stir to coat, adding enough reserved pasta water to make a creamy sauce. Stir in beans and heat over medium until warmed through. Season with salt and pepper. To serve, sprinkle with Parmesan, if desired.