Start by bringing a large pot of salted water to a boil. Cook the fettuccine according to the package instructions until it’s al dente. Reserve a cup of the pasta water before draining the noodles. Keep the drained pasta warm while you prepare the sauce.
While the pasta cooks, heat the butter in a medium saucepan over medium-low heat. Add the heavy cream and stir until well combined. Sprinkle in the kosher salt, black pepper, and nutmeg for an aromatic boost. Allow the mixture to gently simmer, stirring frequently, until it thickens slightly. You’ll know it’s ready when it can coat the back of a spoon.
Transfer the cooked pasta back to the pot and pour the luscious Alfredo sauce over it. Toss the pasta to ensure each strand is coated evenly. Add the shredded rotisserie chicken and sprinkle in the Parmesan cheese. If the sauce feels too thick, gradually add the reserved pasta water, a little at a time, until you reach your desired consistency.
Once everything is combined, garnish the dish with chopped fresh parsley for a touch of color and flavor. Serve warm with a side salad or crusty bread for a complete meal.