Turn on the Instant Pot and select the sauté function. Add the olive oil and garlic, and sauté for 1-2 minutes, until fragrant.
Add the chicken pieces to the Instant Pot and sauté for 2-3 minutes, until lightly browned on all sides.
Add the chicken broth to the Instant Pot and stir to combine.
Break the fettuccine noodles in half and arrange them in a layer on top of the broccoli. Do not stir.
Secure the lid on the Instant Pot and set the valve to sealing. Cook on high pressure for 5 minutes.
When the cooking time is up, quick release the pressure and remove the lid. Place the broccoli florets on top of the cooked pasta and place the lid back on the Instant Pot. Allow the lid to sit on top without turning the Pot back on for 5 minutes. Remove the lid again and stir.
Add the heavy cream and Parmesan cheese to the Instant Pot, stirring until the cheese is melted and the sauce is creamy. If the sauce is too thick, you can add a little bit of additional chicken broth to thin it out.