01 - Pat the chicken breasts thoroughly dry with paper towels and season both sides evenly with kosher salt and freshly ground black pepper.
02 - Heat the olive oil in a large skillet over medium heat. Sear the chicken breasts for 5 to 6 minutes per side until a golden-brown crust forms and the internal temperature reaches 165°F. Transfer to a plate and tent loosely with foil to keep warm.
03 - In the same skillet, melt the unsalted butter over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant, being careful not to let it brown.
04 - Pour in the chicken broth and heavy cream, stirring constantly to deglaze the skillet and incorporate any browned bits from the bottom of the pan.
05 - Add the Boursin cheese to the skillet, breaking it apart with a spoon. Stir continuously until the cheese has fully melted and the sauce is smooth and homogeneous.
06 - Stir in the chopped chives and parsley. Let the sauce simmer gently for 2 to 3 minutes, allowing it to reduce slightly and thicken to a creamy consistency.
07 - Place the seared chicken breasts back into the skillet, spooning the sauce over each piece. Simmer together for 2 to 3 minutes until the chicken is heated through and evenly coated.
08 - Transfer the chicken to serving plates and spoon the Boursin sauce generously over each breast. Garnish with additional fresh chives if desired and serve immediately.