Pat chicken breasts dry and season generously with salt and pepper on both sides.
Heat olive oil and butter in a large skillet over medium-high heat.
When butter is melted, add chicken breasts and brown on each side (about 6-7 minutes per side) until chicken is cooked all the way through. Remove from pan.
Using same pan and any drippings from the meat, add mushrooms and onions and cook until golden brown and caramelized. You may need to add a little more oil if pan becomes too dry.
Add flour and stir to coat. Cook 1-2 minutes.
Add in chicken broth, heavy cream, worcestershire sauce, and dijon mustard and whisk gently until thickened.
Add salt and pepper to taste.
Place chicken breasts back in the pan and cover with sauce. Allow to heat through.
Plate and spoon sauce over chicken to serve.
Optional: Garnish with fresh thyme and parsley.