Season the chicken breasts with salt and black pepper on both sides.
In a large skillet, heat the olive oil over medium-high heat. Add the chicken breasts and cook for about 6-7 minutes on each side, or until they are golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced mushrooms and cook for about 5 minutes, or until they are browned and tender. Add the minced garlic and cook for an additional minute until fragrant.
Pour in the chicken broth and bring to a simmer. Let it cook for about 3-4 minutes to reduce slightly.
Lower the heat and stir in the heavy cream, thyme, parsley, and Parmesan cheese. Cook for another 2-3 minutes until the sauce is creamy and heated through.
Return the chicken to the skillet, coating it with the creamy mushroom sauce. Cook for an additional 2 minutes to warm the chicken.
Serve the chicken topped with the mushroom sauce and garnish with fresh parsley if desired.