Season both sides of the chicken breasts with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat.
Add the chicken breasts to the skillet and cook for 5-6 minutes on each side, or until golden brown and cooked through. Remove chicken from the skillet and set aside.
In the same skillet, add the sliced mushrooms and cook for 4-5 minutes until they release their moisture and become golden.
Add the minced garlic to the mushrooms and cook for 1 minute until fragrant.
Pour in the chicken broth and stir to deglaze the skillet, scraping up any browned bits from the bottom.
Reduce the heat to medium and stir in the heavy cream, grated Parmesan cheese, dried thyme, and butter. Cook for 3-4 minutes, stirring frequently, until the sauce thickens slightly.
Return the cooked chicken breasts to the skillet, spooning the creamy mushroom sauce over them.
Simmer for an additional 2-3 minutes to heat the chicken through and meld the flavors.
Sprinkle chopped fresh parsley over the top before serving.