Season chicken breasts on both sides with salt and black pepper.
Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat.
Sear chicken for 5 to 7 minutes per side until golden brown and the internal temperature reaches 165 degrees Fahrenheit. Remove chicken from skillet and set aside.
In the same skillet, add the remaining 1 tablespoon of butter and minced garlic; sauté for 1 minute until fragrant.
Whisk in chicken broth and heavy cream, scraping the bottom of the pan to deglaze.
Add the Boursin cheese to the skillet and whisk until melted and the sauce is smooth.
Stir in the baby spinach and cook until just wilted, approximately 2 minutes.
Return the chicken to the skillet and spoon the sauce over the breasts. Serve immediately.