Season the cubed chicken generously with salt and pepper.
Heat the olive oil in a 6-quart Dutch oven over medium-high heat.
Add the seasoned chicken and brown on all sides, about 3–5 minutes, without fully cooking through.
Add the minced garlic and sauté about 30 seconds until fragrant.
Pour in the chicken broth and heavy cream, then add the fettuccine and the basil sprig. Bring to a boil.
Reduce heat to a simmer and cook, stirring occasionally, until the pasta is tender, about 15–20 minutes.
When the pasta is done, stir in the frozen peas and cook 1 more minute to heat through.
Remove the basil sprig, stir in the grated Parmesan until the sauce is smooth, and adjust seasoning with salt and pepper if needed.