Bring a large pot of salted water to a boil. Add penne and cook 5 minutes.
Add broccoli and cook until pasta is just under al dente and broccoli is crisp-tender and bright green, 3 to 4 minutes more.
Drain, then add pasta and broccoli back to pot. Toss with garlic, oil, lemon zest and juice, and cheese. Serve, topped with more cheese.
