Season chicken breasts on both sides with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Add the chicken and cook for 5–6 minutes per side, or until golden and cooked through. Remove from skillet and set aside.
Lower heat to medium. Add garlic to the skillet and sauté for 1 minute until fragrant. Stir in the chicken broth and scrape up any browned bits from the bottom.
Add Boursin cheese and heavy cream to the skillet. Stir until the cheese melts and the sauce becomes smooth and creamy.
Add the chicken back to the pan, spoon the sauce over each piece, and simmer for 2–3 minutes to heat through and let the flavors meld.
Garnish with fresh parsley if desired and serve warm over mashed potatoes, pasta, rice, or steamed vegetables.