Season chicken breasts with salt and pepper.
Heat olive oil and butter in a large skillet over medium heat.
Add chicken and sear on each side until golden brown and cooked through (about 6-7 minutes per side). Remove and set aside.
In the same skillet, sauté shallot until translucent, then add garlic and cook for 1 minute.
Reduce heat to low. Add chicken broth, heavy cream, and Boursin cheese. Stir until the sauce is smooth.
Return the chicken to the skillet and spoon the sauce over the top.
Simmer for 2-3 minutes until everything is heated through.
Garnish with chopped parsley and serve warm.