Bring a large pot of salted water to a boil. Add the fettuccine pasta and cook according to package instructions until al dente. Reserve about 1 cup of the starchy pasta water, then drain the pasta.
In a skillet or saucepan over medium heat, melt the unsalted butter. Allow it to bubble gently, but do not let it brown.
Once the butter has melted, add the reserved starchy pasta water to the skillet. Stir to combine, then gradually add in 1 cup of the freshly grated Parmesan cheese, whisking continuously until the cheese has melted and the sauce is smooth.
Taste the sauce and season with kosher salt and freshly ground black pepper to your liking.
Add the drained fettuccine to the skillet with the sauce. Toss the pasta in the sauce until it is fully coated.
Remove the skillet from heat and serve immediately. Garnish with additional Parmesan cheese and chopped fresh Italian parsley.
