Serves: 4 people. Preparation time: 30 minutes.
Trim the steaks of all outside fat. Cut the steaks in half horizontally, making 4 thin pieces. Cover them with plastic wrap and with a mallet, pound the steaks lightly to flatten them to ¼-½ inch thick. This will also tenderize them. Season on both sides with salt and freshly ground black pepper.
Heat a large skillet until a drop of water dances on the surface (medium-high heat), then add 2 tablespoons of the butter. Allow butter to melt and cook for a few seconds. Add the steaks and cook on each side for 1 minute. Remove the steaks from the skillet and lower the heat to low. Wait for the skillet to cool down.
Add 2 tablespoons of butter and the shallots. Sauté the shallots for 1 minute. Increase the heat to high again. Allow the skillet to warm. Carefully add 3 oz. of cognac and tip the skillet to bring the liquid to the edge of the pan, near the flame, to flambé (or use a long igniter). Add the white vermouth and with a wooden spoon, scrape brownings to "deglaze" the pan. Add the mustard and steak sauce and stir. Cook for 1 minute or until the liquid is syrup-like. Add the beef broth and boil on high for 1 minute. Add the cream and stir well. Boil for just a few seconds.
Taste for seasoning and add salt and fresh ground pepper to taste. This is traditionally a highly peppered dish. Carefully add 3 oz. of cognac and flame again. Then add the chives. Add the cooked steaks back in, plus any juice and simmer on medium to reheat them, turning 3 or 4 times to get them coated in the skillet sauce.
Place the steaks on the serving plates and drizzle some skillet sauce on each. Garnish if desired.