Trim excess fat and then slice the chicken breast in half lengthwise to equal pieces that are roughly 3/4 to 1-inch in thickness. Season both sides of the chicken with salt, pepper, and garlic powder. Set aside.
In a large skillet, heat oil over medium heat. Cook the chicken (working in batches if necessary) in the skillet until it is cooked through and the internal temperature is 165°. Adjust the heat as necessary to prevent burning and add additional oil if needed. Remove the chicken from the skillet and tent with aluminum foil to keep warm.
Add the butter and melt. Add the chicken broth to the pan and scrape the bottom of the pan to loosen the cooked-on bits.
Bring the broth to a simmer and add cream cheese. Whisk together to combine once melted.
Add mustard and continue to simmer until sauce starts to thicken, stirring frequently. Add salt and pepper to taste.
Once the sauce is thick, return the chicken to the pan and coat with the sauce. Add additional broth if the sauce gets too thick. Serve immediately.
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