Follow the steps in order for the best result.
Begin by combining the salt and pepper in a small bowl. Evenly rub this mixture onto both sides of each filet mignon, ensuring they are well-seasoned.
In a heavy skillet over medium heat, melt one tablespoon of butter. Once melted, add the Dijon mustard and minced shallots to the skillet. Sauté for approximately one minute, until the shallots become fragrant and slightly softened.
Carefully place the seasoned steaks into the skillet. Cook for about three minutes on each side, or until they reach your preferred level of doneness. For a medium-rare finish, aim for an internal temperature of 130-135°F.
Remove the cooked steaks from the skillet and transfer them to a serving platter. Cover loosely with foil to keep them warm while you prepare the sauce.
To the same skillet with the pan drippings, add the remaining tablespoon of butter, lemon juice, Worcestershire sauce, and minced chives. Cook for about two minutes, stirring constantly, until the sauce slightly thickens and the flavors meld together.
Carefully pour in the brandy to the pan. Allow the brandy to heat slightly, then ignite it carefully with a long match or lighter to flambé the sauce. Once the flames subside, the alcohol will have burned off, leaving behind a rich flavor. Alternatively, you can skip the flambé step and simply simmer the brandy in the sauce for about a minute.
Pour the prepared sauce evenly over the steaks on the serving platter. Garnish generously with freshly chopped parsley.
Serve immediately and enjoy this classic Steak Diane for Two!