Take the cream cheese out of the fridge to soften up at least 30 minutes (or longer) prior to starting the recipe, or microwave it for 20-30 seconds. Grate the parmesan cheese. I prep other ingredients while I'm going along.
Boil a large, salted pot of water for the fettuccine. Cook it al dente according to package directions.
Meanwhile, cut the chicken breasts in half lengthwise so you have 4 thinner cutlets. Sprinkle them with the garlic powder and salt & pepper on both sides. Coat them in flour.
In a deep skillet over medium-high heat, add the olive oil and 1 tablespoon of the butter. When the pan is hot, cook the chicken for 5 minutes/side or until golden and cooked through. Take the pan off the heat, and remove the chicken to a plate and set it aside.
Wipe out the skillet/give it a quick rinse if there's a lot of extra grease (no need to wash it unless you really want to). Add in the remaining 2 tablespoons of butter, the cream cheese, cream, chicken broth, and garlic. Return the pan to the burner over medium heat. Once the butter has melted and the pan has heated up, use your spoon to help the cream cheese melt into the sauce. This will take a couple of minutes.
When the cream cheese has been incorporated into the sauce, let it gently bubble for 5 minutes until the sauce has reduced somewhat. You can give it the occasional stir. Slice the chicken into bite-size strips while it's cooking.
Stir the parmesan into the sauce. Let it cook for about a minute. The sauce should be thick enough by now, but if you want to reduce it further, let it cook for a little longer. If at any point the sauce gets too thick, simply add a splash of the hot pasta water to it. Give it a taste and season with salt & pepper as needed.
Drain the fettuccine and add it to the skillet and toss with the sauce. Dish it up with the chicken on top (or mix it in) and grate on more parmesan cheese as desired.