Set the Instant Pot to sauté. Add olive oil and the chicken pieces. Cook until lightly browned on all sides, about 4–5 minutes. Remove the chicken and set aside.
In the same pot, add garlic and sauté for about 30 seconds until fragrant. Be careful not to burn it.
Pour in the chicken broth and deglaze the pot, scraping up any browned bits from the bottom.
Add the broken fettuccine, distributing evenly in the liquid. Layer the chicken back on top.
Pour in the heavy cream. Do not stir vigorously; you want the pasta to cook with the liquid soaking in.
Seal the lid, set the valve to sealing, and cook on high pressure for 6 minutes. It will take a few minutes to come to pressure.
When the timer finishes, perform a quick release. Open the lid carefully.
Stir in parmesan cheese and butter until the sauce thickens slightly. If the sauce is too thin, you can simmer on sauté mode for 1–2 minutes to reduce.
Taste and adjust with salt and pepper. If you like a deeper flavor, a pinch of nutmeg or paprika can be stirred in at the end.
Serve immediately with extra parmesan if desired. The sauce should cling to the pasta and coat each piece of chicken nicely.