Pound the chicken breasts if they are thick to about 1 inch thick. Season with salt and pepper on both sides.
Heat your skillet and put about 1/2 stick of butter in the skillet. Brown the chicken breasts on both sides until lightly brown. Add the mushrooms and cook for about 2 minutes then add the shallots and garlic and cook until fragrant (about a minute). Add 1 cup of the wine and the 1/2 teaspoon of tarragon and turn the heat down to simmer. Simmer for approximately 35 minutes or until very tender.
Remove the fully cooked breasts from your skillet and turn the heat up to medium/high. At this time most of your wine will be cooked down. Add the additional 1 cup of wine and cook for about 3 minutes. Add 1 cup of the whipping cream and let cook for about 5 minutes or until the sauce coats the back of your spoon. Add the remaining butter to make the sauce glossy, stirring the butter in until it completely melts. Return the chicken breasts to the sauce with the mushrooms, shallots and garlic in it and turn the heat to low. Let it simmer for a couple of minutes with the chicken breasts in it. If the sauce gets too thick for your taste, add some additional whipping cream. Garnish with parsley, if desired.
Serve with parmesan couscous or rice, crusty bread and a great salad.