In a large skillet, heat the olive oil over medium-high heat. Season the chicken breasts with salt and pepper, then add them to the skillet. Cook for about 6-7 minutes on each side, or until the chicken is 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 1-2 minutes, until fragrant.
Pour in the chicken broth and bring to a simmer. Allow it to reduce slightly for about 3-4 minutes.
Lower the heat and stir in the heavy cream, dried thyme, dried parsley, and Parmesan cheese. Mix well and let it simmer for another 3-5 minutes until the sauce thickens.
Return the cooked chicken to the skillet, coating it with the creamy mushroom sauce. Cook for an additional 2 minutes to heat through.
Serve the chicken hot, garnished with fresh parsley if desired.