Begin by boiling a pot of salted water for the pasta. Cook the fettuccine according to package instructions until al dente. Reserve ½ cup of pasta water, then drain the pasta and set aside.
In a large skillet, heat the olive oil over medium-high heat. Add the chicken pieces and season them with salt and black pepper. Cook for about 6-8 minutes, or until the chicken is cooked through and golden brown. Remove the chicken from the skillet and set it aside.
In the same skillet, add the minced garlic and sauté for 1 minute until fragrant.
Pour in the chicken broth and bring it to a simmer. Allow it to cook for about 2 minutes to reduce slightly.
Lower the heat and add the heavy cream and Parmesan cheese to the skillet, stirring constantly until the cheese is melted and the sauce is creamy. If the sauce is too thick, add a little reserved pasta water to achieve your desired consistency.
Add the cooked chicken back into the skillet and mix well to coat everything in the sauce. If using, stir in the red pepper flakes for a bit of heat.
Finally, add the cooked fettuccine to the skillet and toss everything together until the pasta is well coated in the creamy sauce.
Serve the pasta hot, garnished with chopped parsley.