Begin by seasoning the chicken breasts with salt and pepper on both sides.
In a large skillet, heat the olive oil over medium-high heat. Add the seasoned chicken breasts and cook for about 5-6 minutes per side, or until golden brown and cooked through. Remove from the skillet and set aside.
In the same skillet, add the chopped onion and sauté for about 3 minutes, until it becomes translucent.
Add the minced garlic and sliced mushrooms, cooking for an additional 5-7 minutes until the mushrooms are tender and browned.
Pour in the chicken broth, scraping the bottom of the skillet to release any browned bits, and allow it to simmer for 2-3 minutes.
Reduce the heat to low and stir in the heavy cream and Dijon mustard. Mix well until combined.
Add the dried thyme and oregano, stirring to incorporate. Let the sauce simmer gently for another 3-4 minutes until it thickens slightly.
Return the chicken to the skillet, spooning the creamy mushroom sauce over the top. Simmer for an additional 5 minutes to allow the flavors to meld.
Taste and adjust the seasoning if needed.
Serve hot, garnished with freshly chopped parsley.