Bring a large pot of generously salted water to a boil and cook the fettuccine according to package directions.
During the last 3–4 minutes of the pasta cooking time, add the broccoli florets to the boiling water and cook until both pasta and broccoli are tender.
Drain the pasta and broccoli in a colander, then return them to the pot and set aside while you make the sauce.
In a medium saucepan over medium heat, melt the butter. Stir in the half and half and bring to a gentle simmer, then cook 5–8 minutes, stirring occasionally, until the mixture is slightly thickened—do not boil.
Whisk in the garlic powder, salt, black pepper, cayenne, and the shredded Parmesan until the cheese melts and the sauce is smooth.
Pour the sauce over the drained fettuccine and broccoli and toss gently with tongs or a pasta fork until everything is evenly coated.
Serve immediately and sprinkle with additional Parmesan if desired.