Start by seasoning both sides of the chicken breasts with salt, pepper, and dried thyme.
In a large skillet, heat the olive oil over medium heat. Once hot, add the seasoned chicken breasts and cook for about 5-7 minutes on each side or until they are golden brown and cooked through. Remove the chicken from the skillet and set it aside.
In the same skillet, add the sliced mushrooms and minced garlic. Sauté for about 5 minutes until the mushrooms are tender and have released their juices.
Reduce the heat to low, and pour in the heavy cream. Stir well to combine with the mushrooms and garlic.
Gradually add the grated Parmesan cheese, stirring continuously until the sauce is creamy and smooth. If the sauce is too thick, you can add a splash of chicken broth or water to reach your desired consistency.
Return the cooked chicken breasts to the skillet, making sure they are coated in the creamy mushroom sauce. Let them simmer for an additional 2-3 minutes.
Adjust seasoning with more salt and pepper if needed.
Serve the creamy mushroom Parmesan chicken hot, garnished with freshly chopped parsley.