Bring a large pot of salted water to a boil. Add the fettuccine and cook until al dente, according to package instructions.
While the fettuccine cooks, melt the butter in a large skillet over low heat.
Add the heavy cream to the skillet with the melted butter and stir to combine. Increase the heat to medium and bring the mixture to a simmer.
Add the Parmesan cheese to the skillet and stir until it's melted and the sauce is smooth.
Season the sauce with salt and pepper to taste.
When the fettuccine is done, reserve 1 cup of the pasta cooking water, then drain the fettuccine and return it to the pot.
Add the Alfredo sauce to the pot with the fettuccine and toss to coat the noodles evenly. If the sauce seems too thick, add a little bit of the reserved pasta cooking water to thin it out.
Serve hot, garnished with chopped fresh parsley, if desired.