**Thicken the cream on the stove, then add the Parmesan and toss with hot pasta.** Cooling can thicken Alfredo a little, but the sauce should already coat a spoon before you serve it.

For a cream-based Alfredo, try this:

1. **Use heavy cream.** Milk or half-and-half will produce a thinner sauce with the same quantities and cooking time.
2. **Gently simmer the cream uncovered before adding cheese.** Stir frequently, scraping the bottom. Judge by consistency: it should coat the back of a spoon. For reference, Jessica Gavin’s recipe reduces 1½ cups of heavy cream to about 1 cup.
3. **Turn off the heat and stir in finely grated Parmesan.** It adds thickness as well as flavor. Avoid a hard boil after adding cheese, which can make the sauce grainy or separate. [Recipe and method](https://www.jessicagavin.com/alfredo-sauce/)
4. **Add the hot, drained fettuccine and toss thoroughly.** Keep reserved pasta water handy; add a tablespoon at a time only if the sauce becomes too thick. Serve immediately in warmed bowls.

Based on your description, insufficient reduction is a likely cause. If the sauce is smooth but milky, reduce the cream more next time. If it has oily puddles or cheese clumps, address the heat and cheese incorporation.

I couldn’t retrieve the linked recipe, so I can’t check its proportions. For preserving the flavor you already like, start by adjusting the reduction step; adding more cheese will also increase saltiness.