Begin by patting the chicken breast cutlets dry with paper towels to remove excess moisture. Season both sides generously with fresh ground salt and pepper. Set aside.

Heat 2 tablespoons of avocado oil in a large skillet over medium-high heat until shimmering. Add the chicken cutlets, cooking for 5-6 minutes on each side until golden brown and an internal temperature of 160-165°F. Transfer to a plate and cover with foil.

In the same skillet, reduce the heat to medium and pour in 1 cup of chicken broth, scraping up the brown bits. Add the Boursin cheese and whisk until smooth. Simmer for 3-5 minutes until thickened.

Stir in the chopped fresh parsley. Return the chicken cutlets to the skillet, spoon the Boursin sauce over them, and warm together for a couple of minutes before serving.