Warm a large pan over medium heat. After the pan is warm, add the butter and tilt the pan so that the butter is distributed all over the bottom of the pan.
Add your chicken breasts. Season the top of the chicken with salt and pepper. If you have thick pieces of chicken breast, put a lid on the pan to help the middle get cooked through. Cook the chicken for 8 minutes per side, or until golden brown and cooked through.
Remove the cooked chicken breast from the pan. Place the chicken on a cutting board, so that you can slice it after it has rested for 10 minutes.
Add the garlic to the skillet for around 30 seconds. You want the garlic to be light brown in color but not burn!
Pour the whole milk and chicken broth into the pan. Season with salt and pepper, based on your preference. Let the sauce warm up to a simmer.
Add the spaghetti or fettuccine to your pan, and continue stirring until it is al dente (around 10-11 minutes, depending on the type of pasta.)
If your sauce is still thin at this point, remove the pasta with cooking tongs. That way the sauce can continue to thicken and cook down, without your pasta getting overcooked!
Once the sauce has thickened a little (about 3-5 minutes usually), add in your heavy cream. Continue to simmer until the sauce has thickened again (another 5 minutes or so).
Add in the Parmesan cheese and cook it over medium-low heat just until the cheese is melted. Do not overcook it!
Toss the pasta back into the pan and mix it with the sauce. Add your sliced chicken on top.
Garnish by sprinkling chopped parsley on top and serve!