01 - Bring a large pot of salted water to a rolling boil over high heat.
02 - Add pasta to boiling water and cook according to package directions until al dente, adding broccoli florets during the final 3 minutes of cooking time.
03 - Before draining, measure out and reserve 1/2 cup of the starchy pasta cooking water, then drain pasta and broccoli thoroughly in a colander.
04 - Heat olive oil in a large skillet over medium heat. Add sliced garlic and red pepper flakes (if using), sautéing for 1 minute until fragrant and lightly golden.
05 - Add drained pasta and broccoli to the skillet. Toss vigorously to coat evenly, incorporating reserved pasta water as needed to achieve a silky, emulsified sauce consistency.
06 - Remove from heat and stir in lemon zest, fresh lemon juice, and Parmesan cheese. Season generously with salt and black pepper to taste.
07 - Transfer to serving bowls, sprinkle with chopped parsley, and offer additional Parmesan cheese at the table.