Pound the chicken breasts to an even thickness. Season with the Cajun seasoning, making sure to coat both sides of the chicken.
Bring a large pot of salted water to a boil.
While the water is heating, heat a large skillet over medium heat. Swirl in the oil to coat the pan.
Add the chicken to the skillet and cook through, flipping halfway through cooking, about 10 minutes.
Remove the chicken from the skillet and place on a cutting board to rest.
Add the fettucine to the boiling water and cook until al dente.
While the pasta is boiling, wipe out the skillet and place it back over medium heat. Add the butter and let melt. Once melted, stir in the garlic and cook for about 1 minute, until fragrant.
Add the heavy cream and cream cheese to the skillet and cook for 2-3 minutes, stirring often, to heat the cream and melt the cream cheese.
Once hot, add the Parmesan and whisk together until the sauce is smooth and combined. It should be creamy and uniform at this point.
Drain the pasta and add it to the sauce. Toss to coat.
Slice or chop the chicken and serve over the pasta with a sprinkling of freshly minced parsley.