Bring a large pot of salted water to a boil. Add penne and cook for 5 minutes.
Add broccoli and cook until pasta is just before al dente and broccoli is bright green, about 3 minutes more. Drain, then add pasta and broccoli back to pot.
Stir in garlic, olive oil, lemon zest, lemon juice and Parmesan cheese.
Serve, topped with additional Parmesan cheese.