Bring a large pot of salted water to a boil. Add the broccoli florets and cook for about 3-4 minutes, until they are bright green and tender. Remove the broccoli with a slotted spoon and set aside. Keep the water boiling for the pasta.
In the same pot of boiling water, cook the pasta according to package instructions until al dente. Reserve about 1 cup of the pasta water before draining (note 1).
While the pasta cooks, in a food processor, blend the cooked broccoli, basil leaves, garlic, pine nuts, parmesan (or nutritional yeast), and sea salt (photo 4). Process until smooth. If the pesto is too thick, you can add a little olive oil or pasta water to reach your desired consistency.
Return the drained pasta to the pot. Add the broccoli pesto and toss to coat the pasta evenly. If the sauce is too thick, add some of the reserved pasta water to loosen it up. Adjust the seasoning with salt if necessary.
Serve the pasta, and if desired, sprinkle with extra grated parmesan and chili flakes for a bit of heat.