Since each pounded, flattened chicken should have a large circumference, it will be necessary to cook the four breasts one at a time, setting each aside on a warm platter as you finish those that remain or use two pans to cook two simultaneously.
Season the chicken with salt and pepper. Heat a large, heavy skillet over medium heat. Add 1/2 tablespoon of butter to the hot pan and heat the butter until it begins to foam. Add the first
breast and sear, cooking for 3 to 4 minutes on a side before turning it over and allowing another 4 minutes on the second side. Remove the chicken from the pan and place on a warm platter. Repeat for the remaining chicken breasts, adding butter to the pan and sauteeing both sides. After all the chicken has been cooked and removed from the pan, add the shallots and cook two minutes until translucent. Lower the heat, move the pan away, and cautiously add the brandy. Being careful not to flame the brandy, return the pan to the stove, and over low heat, allow it to cook off. Add the white wine to the pan, raise the heat, and bring quickly to the boil. Stir in the mustard. Allow this to cook for 1 minute before adding the veal stock. Cook for 2 to 3 minutes more. Add the cream. Bring just to the boil. Remove from the heat and stir in the chives.
Place the ovenproof platter of chicken breasts in a preheated 350 degree oven for 1 to 2 minutes to reheat them very quickly before placing them on individual dishes and topping with some of the Diane Sauce. Serve with garlic mashed potatoes.