Heat the olive oil in a large skillet over medium heat.
Season the chicken breasts with salt and pepper on both sides.
Add the chicken breasts to the skillet and cook for about 5-7 minutes on each side, or until the chicken is golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the diced onion and cook for 3-4 minutes until softened.
Add the minced garlic and sliced mushrooms to the skillet and cook for another 5 minutes, stirring frequently, until the mushrooms are tender.
Sprinkle the dried thyme and basil over the mushroom mixture, stirring to combine.
Pour in the chicken broth and bring to a simmer. Let it cook for 2-3 minutes.
Reduce the heat to low and stir in the heavy cream. Mix well until the sauce is creamy and heated through.
Return the chicken breasts to the skillet, coating them in the creamy mushroom sauce. Let them simmer for an additional 5 minutes, allowing the flavors to meld.
Taste and adjust seasoning with additional salt and pepper if needed.
Serve immediately, garnished with fresh parsley if desired.