Cook the pasta according to package instructions, drain, and set aside (reserving at least a cup of the pasta water. Make the chicken while the pasta cooks.
Pat the chicken dry with a paper towel. Season it with salt, then rub both sides with Creole seasoning.
Heat oil in a large pot over medium-high heat. Add the chicken and brown for 4-5 minutes on both sides or until golden brown, and it has cooked through. Be careful so it doesn't burn. Clean the pan if any major burns occur.
Remove chicken from the pan and keep warm by covering it with foil while you prepare the Alfredo sauce.
In the same pan, melt the butter, then add garlic, thyme, and Creole seasoning. Stir for about a minute or until fragrant.
Reduce the heat to as low as possible, and slowly whisk in heavy cream, milk, and cream cheese. Whisk constantly until it starts to thicken.
Stir in the Parmesan cheese and mix until the sauce is smooth or until everything is well combined.
Pour in the chicken stock. Cook over medium heat for 5-6 minutes or until it thickens. Adjust the thickness of the sauce with the reserved pasta water.
Season with salt, pepper, and extra Creole seasoning. Add the drained pasta, and mix well to coat the pasta.
Turn off the heat and let it rest for 5-7 minutes so the pasta can soak up some of the sauce. The sauce will thicken as it cools.
Serve the pasta, top it with sliced chicken breast, and enjoy.