Cooking Chicken: Add salt and pepper to chicken breast. In a big frying pan, warm up olive oil on medium-high heat. Cook the chicken breast until it is golden brown and fully cooked (around 5-6 minutes on each side). Take out of the pan and set aside.
Preparing the sauce: If needed, add a bit more olive oil to the same pan. Cook the onions in a pan until they are soft (approximately 3-4 minutes). Put chopped garlic and sliced mushrooms in the pan and cook them until they turn brown and soft (around 5 minutes).
Combine ingredients: Pour in chicken broth and heat until it starts to simmer, making sure to scrape off any brown bits stuck to the bottom of the pan. Add heavy cream, Dijon mustard, and thyme and mix well. Let it cook for around 5 minutes until the sauce thickens slightly.
Finish the dish: Return the chicken breasts to the pan so they are covered in sauce. Cook gently for another 2-3 minutes until the chicken is warm and the flavors mix together. If needed, try the food and add more salt and pepper to adjust the flavor.
Serve: Before serving, add some chopped fresh parsley on top. To savor the dish "Savvy Chicken Pleasure," serve it hot with rice, pasta, or crusty bread to soak up its delicious sauce.