Prep Chicken: Pat the thinly sliced chicken cutlets dry and season lightly with salt and pepper on all sides.
Cook Chicken: Heat the oil in a large skillet over medium-high heat until shimmery. Cook the chicken for about 5-6 minutes per side or until cooked through (160-165°F internally or no more pink inside). If the oil splatters or chicken is cooking too fast on the outside, turn down the heat and cover with a lid as needed. When done, transfer the chicken to a plate and set aside.
Make Gravy: Add the chicken broth and Boursin cheese (break it up into crumbles) to the skillet. Whisk until smooth, scraping up the brown bits from the bottom to add flavor. Turn down the heat to medium-low and gently simmer the sauce for 3-5 minutes. Stir in the chopped parsley.
Finish & Serve: Turn the heat to low. Add the chicken and any plate juices back into the skillet, spoon the sauce over it, and let it warm through for a couple of minutes. If the sauce gets too thick, whisk in another splash of chicken broth. Taste and adjust seasoning, as needed, and serve warm immediately.
