Cook the pasta
Bring a large pot of salted water to a boil. Add the pasta and cook until al dente according to the package directions.
Before draining, reserve a small splash of pasta water in case you need to loosen the sauce later.
Start the sauce
While the pasta cooks, melt the butter in a large skillet over medium heat.
Sprinkle in the flour and whisk for about 1 minute. This creates a quick base that helps the cream sauce turn smooth and lightly thickened.
Add garlic and lemon
Stir in the minced garlic and cook briefly until fragrant.
Pour in the chicken broth, vegetable broth, or dry white wine. Add the lemon juice and lemon zest, then let the mixture simmer for about 1 minute so the flavors can concentrate.
Make it creamy
Reduce the heat slightly and stir in the heavy cream.
Add the cooked chicken and let it warm through in the sauce. Simmer gently for a few minutes, stirring often, until the sauce looks glossy and slightly thickened.
Finish with parmesan
Remove the skillet from the heat and stir in the parmesan cheese.
Taste and season with salt and black pepper as needed. The parmesan adds saltiness, so adjust carefully.
Toss with pasta
Add the drained pasta to the skillet and toss until every strand or piece is coated in the creamy lemon sauce.
If the sauce feels too thick, add a small splash of reserved pasta water and toss again.
Serve warm
Serve right away with extra parmesan, chopped parsley, and a little fresh lemon if you want a brighter finish.