Heat the olive oil in a skillet over medium heat. Add the chicken and cook until it's no longer pink in the center. Remove from the skillet and set aside.
In the same skillet, add the broccoli and cook until it's bright green and slightly crisp. Remove from the skillet and set aside.
Cook the fettuccine according to the package instructions. Drain, reserving a cup of pasta water.
In the same skillet, add the heavy cream. Bring to a simmer and gradually add the cheese, stirring until it's melted and smooth.
Add the cooked chicken, broccoli, and pasta to the skillet. Toss to coat everything in the sauce. If the sauce is too thick, add a bit of the reserved pasta water. Serve hot.
Notes
Make sure to season your chicken well before cooking. It's the base of your flavor profile.
Don't overcook your broccoli. It should be vibrant green and slightly crisp.
Cook your pasta al dente (firm to the bite) as it will continue to cook a bit in the sauce.
Gradually add the cheese to your sauce while stirring to avoid clumping.
If your sauce gets too thick, you can thin it out with a little pasta water.