Boil a large pot of salted water and cook the fettuccine according to package instructions.
Season the chicken breasts with salt and pepper.
Heat olive oil in a large skillet over medium heat and add the chicken.
Cook the chicken for 6-7 minutes on each side until browned and cooked through.
Remove the chicken from the skillet and let it rest before slicing.
Add butter to the same skillet and sauté minced garlic until fragrant.
Pour in the heavy cream and bring to a simmer, stirring frequently.
Stir in grated Parmesan cheese until melted and smooth.
Add the broccoli florets and cook until tender, about 4-5 minutes.
Drain the pasta and combine it with the Alfredo sauce, mixing well.
Slice the chicken and serve it on top of the pasta and broccoli, garnished with parsley.