Slice the chicken breasts into thin strips and season generously with Cajun seasoning, ensuring each piece is well coated.

Cook the fettuccine according to package directions until al dente, then drain and set aside, reserving a bit of the pasta water.

Heat olive oil in a large skillet over medium-high heat, then add the seasoned chicken and cook until browned and cooked through, about 5-7 minutes; remove chicken from the skillet and set aside.

In the same skillet, melt butter over medium heat and sauté minced garlic for about 1 minute until fragrant.

Pour in the heavy cream and chicken broth, bring the mixture to a simmer, and stir in the grated Parmesan cheese until the sauce is smooth and slightly thickened.

Return the cooked chicken to the skillet with the sauce, add the cooked fettuccine, and toss everything together to coat the pasta evenly.

If the sauce is too thick, add a small amount of the reserved pasta water to reach your desired consistency; season with salt and black pepper to taste.

Serve immediately, garnished with fresh chopped parsley.