Add pasta to a large pot of boiling, salted water. Cook according to package directions.
While still cool, add olive oil, butter, red pepper flakes, and lemon zest to a large sauté pan.
Place sauté pan over very low heat, allowing butter to melt and lemon zest to infuse the olive oil mixture.
Approximately 4 minutes before pasta is cooked, add broccoli florets to boiling pasta pot. Cook broccoli and pasta together until pasta is al dente.
At the same time, increase heat under sauté pan to medium high
Add garlic to olive oil and sauté for 2 or 3 minutes.
Add lemon juice to finish the sauce.
Drain pasta and broccoli, then add to both to the sauce.
Remove from heat.
Toss with parmesan cheese and lemon slices (if desired).