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 sauté for 5-6 minutes until they are browned and tender. Add the minced garlic and cook for an additional 1 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, dried thyme, dried parsley, and grated Parmesan cheese. Mix well and let it simmer for another 3-4 minutes until the sauce thickens.
Return the chicken to the skillet, coating it in the creamy mushroom sauce. Cook for an additional 2-3 minutes to heat through.
Serve hot, garnished with fresh parsley.