In a large skillet, heat the olive oil over medium heat. Season the chicken breasts with salt and pepper, then add them to the skillet. Cook for about 5-7 minutes on each side until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the mushrooms, onion, and garlic. Sauté for about 3-4 minutes until the vegetables are softened.
Pour in the chicken broth and bring to a simmer. Allow it to cook for 2-3 minutes to reduce slightly.
Stir in the heavy cream, thyme, parsley, and Parmesan cheese. Cook for another 3-4 minutes until the sauce thickens.
Return the chicken to the skillet, spooning the sauce over the top. Drizzle with lemon juice and let it simmer for an additional 2 minutes.
Serve hot over rice or pasta, garnished with extra parsley if desired.