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 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 minute until fragrant.
Pour in the chicken broth, scraping the bottom of the skillet to release any browned bits. Bring to a simmer and let it cook for 3-4 minutes.
Reduce the heat to low and stir in the heavy cream, dried thyme, and dried parsley. Allow the sauce to simmer for another 5 minutes until it thickens slightly.
Stir in the grated Parmesan cheese until melted and well combined. Return the chicken to the skillet, spooning the sauce over the top. Cook for an additional 2-3 minutes to heat through.
Serve the creamy mushroom chicken warm, garnished with fresh parsley if desired.