Season chicken generously with salt and pepper. Add oil to a Dutch Oven or a medium size pot and heat it over medium high heat. Add chicken and brown it on all sides, but not cooked through.
Add garlic and sauté for 30 seconds until fragrant. Add chicken broth, heavy cream, pasta and basil sprig. Bring to a boil, then reduce to a simmer.
Cook for about 15 to 20 minutes or until pasta is tender, stirring occasionally. When pasta is cooked to your liking add frozen peas and cook for 1 more minute. Stir in Parmesan cheese and season with salt and pepper if needed.
Leftovers: Transfer the fettuccine Alfredo into an airtight storage container and let it cool completely before freezing or refrigerating. You can refrigerate up to 5 days or freeze for up to 1 month. Something to note, you may find a skin texture form over your sauce that resembles a paste-like consistency; this is normal!
Reheating leftovers: I recommend reheating your leftovers in a pan over low heat. Microwaving may leave your noodles with a too-soft texture and sauce may be greasy rather than creamy.