Season the chicken cutlets with salt and pepper.
Heat olive oil in a skillet over medium high heat and melt the butter.
Add the chicken to the skillet and cook for 3 to 4 minutes per side or until cooked through (165°F/74°C Internal temp). Remove onto a plate and cover with foil to keep warm.
Deglaze the skillet with a little chicken stock, then add the rest of the stock and let it simmer.
When it starts simmering, add the Boursin cheese and stir it with a spatula. As it warms up, it will melt into the stock and create a sauce.
Stir in the Dijon mustard then simmer the sauce for a couple of minutes so it thickens.
Add the chicken back in, spoon the sauce over the chicken, and serve over mashed potatoes and broccoli or green beans.