Season the chicken breasts with Cajun seasoning, ensuring they are evenly coated.
In a large skillet, heat the olive oil over medium-high heat. Add the seasoned chicken and cook for about 6-7 minutes on each side, or until the chicken is cooked through and has a nice golden brown color. Remove from the skillet and let rest for a few minutes before slicing.
While the chicken is resting, cook the fettuccine pasta according to package instructions until al dente. Drain and set aside.
In the same skillet, reduce the heat to medium and add the minced garlic. Sauté for about 1 minute until fragrant.
Pour in the heavy cream and bring to a simmer. Stir in the grated Parmesan cheese until melted and smooth. Season with salt and pepper to taste.
Add the cooked fettuccine to the sauce, tossing to coat the pasta evenly. Slice the chicken and place it on top of the pasta.
Garnish with chopped fresh parsley before serving.