Fill large pot with salted water. Bring to a boil.
While the pasta water gets underway, begin sauce. In a small sauce pan over medium heat, melt butter. Add garlic and cook for two minutes. Then add in heavy cream and cream cheese. Heat until bubbling, but do not boil. Slowly add in Parmesan cheese while stirring. Mix until the cheese melts. Keep warm on low heat, stirring occasionally. Add salt and pepper to taste.
Once pasta water is ready, place the fettuccine noodles in the boiling water. Boil for 11 minutes.
While pasta and sauce cook, prep and cook chicken cutlets. Heat oil in a skillet. Salt and pepper each side of chicken cutlets. Add chicken to pan. Don't overcrowd. May need to cook in batches. Cook until internal temperature reads 165F, 3-5 minutes per side.
Once pasta is ready, drain, preserving some of the pasta water. Add Alfredo sauce to the pasta. Toss and add a splash of the reserved pasta water. Toss until mixed.
When chicken is ready, serve sauced pasta and top with sliced chicken, and a sprinkle each of Parmesan and parsley.