Warm olive oil in a small frying pan over low heat. Slowly cook garlic in oil until golden, about 2 to 3 minutes. Be very careful not to burn garlic. Stir in lemon juice, and season with salt and pepper.
Meanwhile, cook pasta in a large pot of boiling salted water. About 5 minutes before pasta is done, drop broccoli into the pasta water. Continue to cook until pasta is cooked and broccoli is crisp-tender. Drain.
Toss pasta, broccoli, and lemon sauce in a large bowl. Sprinkle with grated Parmesan cheese.