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 breasts and cook for about 6-7 minutes on each side, or until the chicken is cooked through and has a nice golden color. Remove the chicken from the skillet and let it rest for a few minutes before slicing it into strips.
While the chicken is resting, cook the fettuccine according to package instructions in a large pot of salted boiling water. Drain and set aside.
In the same skillet used for the chicken, melt the butter over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant.
Pour in the heavy cream and bring to a gentle simmer. Stir in the grated Parmesan cheese until melted and smooth. Season with salt and pepper to taste.
Add the cooked fettuccine to the skillet and toss to coat in the creamy sauce.
Serve the pasta topped with sliced Cajun chicken and garnish with chopped parsley.