Season both sides of the chicken breasts with salt, pepper, and dried thyme.
Heat olive oil in a skillet over medium-high heat until shimmering and fragrant.
Carefully place the chicken breasts into the hot skillet and sear for 4-5 minutes without moving, until golden brown on the underside.
Flip the chicken and cook for another 4-5 minutes until the second side is golden and the chicken is cooked through.
Remove the chicken from the skillet and set aside to rest. Pour chicken broth into the same skillet, scraping up any browned bits from the bottom.
Add the minced garlic to the skillet and cook for about 30 seconds until fragrant, stirring constantly.
Whisk in the Boursin cheese until smooth and melted, creating a creamy sauce.
Return the chicken to the skillet, spooning the sauce over the top. Simmer for 5 minutes to reheat and meld flavors.
Serve the chicken topped with the velvety herb-infused sauce, garnished with additional herbs if desired.