Prepare the Chicken: Season the chicken breasts with salt and pepper on both sides.
Cook the Chicken: In a large skillet, heat the olive oil over medium heat. Add the chicken breasts and cook for about 6-7 minutes on each side, or until fully cooked. Remove the chicken from the skillet and set aside.
Sauté the Mushrooms: In the same skillet, add sliced mushrooms. Cook for 5-6 minutes, until they are golden brown. Stir in the minced garlic and cook for another minute.
Make the Sauce: Pour in the chicken broth, Dijon mustard, and thyme. Bring to a simmer and let it cook for about 3-4 minutes. Then, add the heavy cream and simmer for another 5 minutes, or until the sauce thickens.
Combine: Return the cooked chicken to the skillet and cook for an additional 2-3 minutes, allowing it to soak up some sauce.
Serve: Garnish with fresh parsley and serve warm with your choice of sides, such as rice, pasta, or steamed vegetables.