Reserve about 1/3 cup of the grated Parmesan cheese and set aside for serving.
Bring a large pot of generously salted water to a boil and cook the fettuccine according to the package directions until al dente.
While the pasta cooks, heat the heavy cream in a deep sauté pan or Dutch oven over low–medium heat until it begins to steam but not boil.
Add the cubed unsalted butter to the warm cream and whisk gently until the butter is melted and the mixture is slightly reduced, 2–4 minutes.
Sprinkle in most of the grated Parmesan (reserve the 1/3 cup) and whisk until the cheese melts and the sauce thickens.
Whisk in the pizza seasoning, then season the sauce with salt and freshly cracked black pepper to taste.
When the pasta is done, reserve about 1/2 cup of the pasta cooking water, then drain the noodles.
Add the drained fettuccine to the sauce and toss to combine; add reserved pasta water a little at a time as needed to loosen the sauce to your desired consistency.
Serve topped with the reserved grated Parmesan, chopped parsley, and lemon wedges for squeezing over individual portions.