For the Alfredo sauce, melt butter over low heat in a small saucepan. Add the cream, stir until blended. Add white pepper (I use 1-2 tsps; you may prefer more or less). Grate in Parmesan cheese and stir slowly as cheese melts and blends in. Keep the heat low (never let it boil) and keep stirring — it takes a while to melt and blend in the cheese.
While the sauce is cooking, bring salted water to a boil in a large pot and add the fettuccini. Cook until al dente, drain, place in a casserole dish and add Alfredo sauce. Toss until the fettuchini is well coated. Garnish with fresh parsley if desired, or serve as is.
You can use half-and-half if you prefer, but plain milk is IMHO too thin. It’s easier to use dried grated Parmesan, but it’s much more tasty if you grate your own.