Bring a large pot of salted water to a boil over high heat. Add the pasta and cook according to the package directions, setting a timer for the lower end of the cooking time minus 4 minutes. (So, if it says the pasta cooks in 10 to 12 minutes, set the timer for 6 minutes.)
When the timer goes off, add the broccoli to the pot with the pasta.
Reserve ½ cup cooking water. (I ladle it out into a small measuring cup or bowl.)
Drain the pasta and broccoli, transfer to a large bowl, and add the butter, Parmesan, lemon juice, lemon zest, and reserved cooking water.
Season the pasta with salt and pepper.
Serve the pasta with additional Parmesan, if desired.