Season the chicken breasts with salt and pepper on both sides.
Heat the olive oil in a large skillet over medium-high heat. Add the chicken breasts and cook for about 6-7 minutes per side, or until they are golden brown and cooked through. Remove the chicken from the skillet and set aside.
Cook the Mushrooms:
In the same skillet, add the butter. Once melted, add the sliced mushrooms and cook until they are browned and softened, about 5-6 minutes.
Add the chopped onion and cook for another 3-4 minutes until the onion is translucent.
Add the minced garlic and cook for an additional 1-2 minutes until fragrant.
Make the Sauce:
Pour in the white wine, stirring to scrape up any browned bits from the bottom of the skillet. Let the wine simmer for about 3-4 minutes to reduce slightly.
Add the chicken broth and dried thyme. Bring the mixture to a simmer and let it cook for another 5-6 minutes.
Finish the Sauce:
Stir in the heavy cream and let the sauce simmer for an additional 2-3 minutes, or until it thickens to your desired consistency.
Return the chicken breasts to the skillet, spooning some of the sauce over them. Let them heat through for about 2-3 minutes.
Serve:
Garnish with fresh parsley and serve the chicken with the mushroom wine sauce. This dish pairs well with rice, mashed potatoes, or a side of vegetables.