Season the chicken breasts on both sides with salt and black pepper.
In a large skillet, heat olive oil over medium-high heat. Sear chicken for 5 to 7 minutes per side until golden brown and cooked through (internal temperature 165°F). Remove chicken and set aside on a plate.
Lower heat to medium and add butter to the same skillet. Once melted, add the mushrooms and sauté for 8 to 10 minutes until they release moisture and become very soft.
Add the minced garlic and dried thyme to the mushrooms; cook for 1 minute until fragrant.
Deglaze the skillet with chicken stock, scraping any browned bits from the bottom. Pour in the heavy cream.
Bring the sauce to a gentle simmer and cook for 3 to 5 minutes until the liquid thickens slightly.
Whisk in the Parmesan cheese until smooth and incorporated.
Return the chicken and any collected juices to the skillet. Simmer for 2 minutes to coat the chicken in the sauce.
Garnish with fresh parsley before serving.