Bring a large pot of salted water to a boil. Add the linguini and cook until al dente according to package directions. Before draining, carefully reserve 1 cup of the pasta water. Drain the pasta and set aside.

While the pasta cooks, place a large nonstick skillet over medium heat. Add the butter and allow it to melt completely.

Sprinkle in the flour and whisk continuously for 1 to 2 minutes, until lightly golden and smooth.

Slowly pour in the chicken broth while whisking constantly to prevent lumps. Once smooth, slowly whisk in the heavy whipping cream. Continue cooking, stirring frequently, until the sauce thickens enough to coat the back of a spoon.

Reduce the heat to low and stir in the Parmesan cheese until completely melted and smooth.

Add the reserved pasta water, a little at a time, stirring after each addition, until the sauce reaches your desired consistency. Let everything simmer together for 3 to 5 minutes, or until the chicken is heated through and the pasta is fully coated.

Sprinkle with chopped parsley and additional freshly shredded Parmesan cheese just before serving.