Season the chicken: Pat the chicken dry with paper towels and season both sides with salt and pepper.
Sear the chicken: Heat olive oil in a large skillet over medium heat. Add the chicken and cook for 5-6 minutes on each side, or until golden and cooked through. Remove and set aside.
Sauté the mushrooms: In the same skillet, melt the butter. Add the sliced mushrooms and cook for 5-6 minutes until browned and tender.
Add garlic and herbs: Stir in the minced garlic and thyme, and cook for about 1 minute until fragrant.
Make the sauce: Pour in the chicken broth to deglaze the pan, scraping up any bits from the bottom. Stir in the heavy cream and bring to a gentle simmer.
Add the Parmesan: Reduce heat to low and stir in the grated Parmesan cheese until melted and smooth. Let the sauce simmer for 2-3 minutes to thicken slightly.
Return the chicken: Place the chicken back into the pan, spooning the sauce over the top. Let everything simmer together for 5 more minutes.
Finish and serve: Sprinkle chopped parsley over the top and serve hot with your favorite side.