Grate the 5.3 ounces Parmesan and set aside about 1/3 cup for garnish; keep the remaining grated cheese for the sauce.
Bring a large pot of heavily salted water to a rolling boil and cook 16 ounces dried fettuccine according to the package instructions until al dente.
Before you drain the pasta, reserve about 1/2 cup of the hot pasta cooking water, then drain the fettuccine.
While the pasta cooks, pour 1 pint heavy cream into a deep sauté pan or Dutch oven and place over low–medium heat. Add 1/2 cup unsalted butter (cubed and softened) and whisk gently until the butter melts. Keep the heat low–medium so the cream does not boil.
Let the cream mixture simmer for a few minutes, until it has slightly reduced and thickened.
Remove the pan from direct high heat or reduce heat to low, then sprinkle in the remaining grated Parmesan (the portion not reserved) and whisk or stir until the cheese has melted and the sauce is smooth. Whisk in 1 1/2 teaspoons pizza seasoning.
Taste the sauce and season with salt and freshly cracked black pepper as needed.
Add the drained fettuccine to the sauce and toss to coat evenly. If the sauce is too thick, add a few tablespoons of the reserved pasta water at a time until you reach your desired consistency.
Serve immediately, garnishing each portion with the reserved 1/3 cup Parmesan, chopped fresh flat-leaf parsley, and lemon wedges for squeezing over the pasta.