Season the cubed chicken generously with salt and black pepper.
Heat the olive oil in a 6‑quart Dutch oven over medium‑high heat. Add the chicken and brown on all sides, about 4–5 minutes, without cooking through.
Add the minced garlic to the pot and sauté for about 30 seconds until fragrant.
Pour in the chicken broth and heavy cream, add the fettuccine (break in half if needed to fit) and the basil sprig, then bring the mixture to a boil.
Reduce heat to a simmer and cook, stirring occasionally, until the pasta is tender and most of the liquid is absorbed, about 15–20 minutes.
When the pasta is cooked to your liking, stir in the frozen peas and cook for 1 minute until heated through.
Remove the basil sprig, stir in the grated Parmesan until melted and the sauce is creamy, and taste to adjust salt and pepper as needed.
Serve immediately, tossing to coat the pasta in the sauce.