Trim all the outside fat off the steak. The steak should now weigh about 12 ounces.
Cut the steak in half horizontally, creating two 6-ounce steaks. Pound the steaks lightly to flatten them to ¼-inch thick. Season them liberally on both sides with salt and freshly ground black pepper.
Heat a 12-inch skillet until a drop of water dances on the surface. Add 1 tablespoon of the butter. As soon as the foam subsides, add the seasoned meat. Cook on each side for 1 minute. Remove to a plate.
Immediately adjust the heat under the pan to low. Add the second tablespoon of butter and the shallots. Sauté the shallots for 1 minute.
Increase the heat to high. Add 3 tablespoons cognac and flambé, if desired. Add the wine and with a wooden spoon scrape up any browning in the pan (deglaze the pan). Stir in the mustard and A-1 sauce. Cook for about a minute, or until the liquid is reduced to a syrup.
Add the broth and continue to boil for about a minute, until reduced to a few tablespoons. Add the cream and stir well to incorporate. Boil a few seconds. Taste for seasoning and add freshly ground pepper to taste.
Add the remaining cognac and ignite.
When the flames die down, stir in the chives, taste for salt and pepper, and adjust if necessary.
Add the reserved steaks and their juices (that have accumulated on the plate) to the simmering sauce. Turn the steaks in the sauce a couple of times, as the sauce reduces a little more.
Place the steaks on individual plates. Divide the sauce on the steaks.
Serve with mashed potatoes or rice, or at least some bread to mop up the sauce.