Bring a large pot of water to a boil and cook the 8 ounces of pasta until al dente according to package directions. Before draining, reserve some of the hot pasta cooking water, then drain the pasta.
When the pasta has about 2 minutes left on its cooking time, start the sauce: melt 1 tablespoon butter in a skillet over medium heat.
Add 1 teaspoon flour to the melted butter and cook, stirring often, for about 2 minutes to form a light roux.
Add 2–3 minced garlic cloves and 1/4 cup chicken broth to the roux; stir and let it simmer for about 1 minute.
Whisk in 1 cup heavy (whipping) cream and continue to cook over medium to medium-low heat, stirring occasionally, until the sauce thickens to your liking (a few minutes).
Stir in 1/3 cup freshly grated Parmesan cheese until melted and smooth. Season the sauce with salt and pepper to taste.
Add the drained pasta to the skillet and toss to coat evenly with the sauce. If the sauce is too thick, loosen it with a little of the reserved pasta water until you reach the desired consistency.
Serve immediately, garnishing with chopped fresh parsley and extra Parmesan if desired.