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 5-7 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 chopped onion and sliced mushrooms. Sauté for about 5 minutes until the onions are translucent and the mushrooms are browned.
Add the minced garlic to the skillet and cook for an additional minute until fragrant.
Pour in the chicken broth, scraping up any browned bits from the bottom of the skillet. Bring to a simmer and let it cook for 3-4 minutes.
Stir in the heavy cream, soy sauce, and dried thyme. Let the mixture simmer for another 5 minutes until it thickens slightly.
Return the chicken to the skillet, coating it in the mushroom gravy. Cook for an additional 2-3 minutes to heat through.
Serve the chicken topped with mushroom gravy and garnish with fresh parsley.