Bring a large pot of water to boil. Add pasta and cook according to package directions, subtracting 2 minutes. When draining, remove one cup of pasta cooking water and set aside.
Liberally season the chicken breasts on both sides. In a pan, heat the extra virgin olive oil over medium-high heat. Add the seasoned chicken and cook on both sides for 5-7 minutes (until it reaches an internal cooking temperature of 165 degrees F.
Over medium heat, melt butter. Add garlic and onion, cook for 3 - 4 minutes until onion is light golden and soft.
Add cream, about ¾ cup pasta water and parmesan. Stir, then simmer for 2 minutes until it reduces slightly - you don’t need to be exact here. Season with salt and pepper.
Add pasta and toss gently in the sauce for about 1 ½ minutes. The sauce will thicken and coat the pasta, do this step until you get the sauce consistency you want. If your sauce gets too thick, add a splash of pasta water.
Garnish with additional parmesan cheese and parsley.