In a large skillet, heat the olive oil over medium-high heat. Season the chicken breasts with salt and pepper, then add them to the skillet. Cook for about 5-6 minutes on each side until 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, cooking for an additional 5 minutes until the mushrooms are browned.
Pour in the chicken broth and white wine, scraping the bottom of the skillet to release any browned bits. Stir in the Dijon mustard, tomato paste, and dried thyme. Bring the mixture to a simmer.
Return the chicken to the skillet, spooning some of the sauce over the top. Cover and let simmer for 10 minutes to allow the flavors to meld.
Before serving, sprinkle with fresh parsley for garnish.