Salt and pepper the breasts of chicken, then cut them lengthwise. Once they are sliced, heat olive oil on medium heat to brown both sides. Transfer to a platter. (At this stage, the chicken will not have been cooked through.
Add the mushrooms to the same saucepan along with the chopped rosemary and salt and pepper. Brown the mushrooms on medium heat for 2 to 3 minutes. Next, add the chopped shallots, minced garlic, and cook for another 2 minutes. Stir in one tablespoon of flour. Next, add the white wines and scrape down the bottom of the pan to remove any brown bits. Add chicken stock, heavy cream, 1 tbsp mustard, and mix to combine.
Add the chicken breasts and the juices back to the saucepan. The sauce should come to a boil. Once it has boiled, reduce the heat to low and simmer for 10 minutes. You can taste the sauce, and adjust the seasonings if needed.