In a clean skillet or the same pan used for the chicken, melt the butter for the alfredo sauce.
Once the butter has melted and starts to bubble just a bit, add the garlic and saute for 30-60 seconds until fragrant.
Slowly add the heavy cream while stirring. Season with the salt, black pepper, and cayenne pepper. Let this cook over medium heat for 2-3 minutes until the cream is just starting to bubble around the edges, but do not let the cream come to a boil.
Reduce the heat to medium low, then sprinkle the freshly grated parmesan cheese over the sauce, stirring while adding until the cheese is melted in. If the sauce isn't thick enough, let it sit for 2-3 minutes off the heat to thicken slightly.
Remove from the heat and toss with fettucine, tortellini, or other pasta and serve.