Two 6-ounce filet mignon steaks, about 1 1/4 inches thick
1/4 cup Cognac
1 tablespoon unsalted butter
1 tablespoon vegetable oil
1/2 teaspoon coarsely ground black pepper
2 large shallots, minced
1/4 cup beef stock or canned broth
Sprinkle the steaks with 1 tablespoon of the Cognac and let stand at room temperature for 45 minutes.
In a heavy medium skillet, melt 1/2 tablespoon of the butter in 1/2 tablespoon of the oil. Rub the steaks on both sides with the pepper. When the skillet is very hot, add the steaks, cover partially, and cook over high heat until a crust forms on the bottom, about 2 minutes. Turn the steaks over and cook, partially covered, until nicely crusted on the other side, about 2 minutes. Continue cooking over moderate heat, turning once, for about 2 minutes per side for medium-rare. Transfer the steaks to a plate and keep warm.
Melt the remaining 1/2 tablespoon butter in the remaining 1/2 tablespoon oil in the skillet. Add the shallots and cook over moderately high heat, stirring frequently, until translucent, about 3 minutes.
Add the remaining 3 tablespoons Cognac to the skillet. Ignite with a match and cook over high heat until the flame burns out, about 30 seconds. Add the beef stock and boil until the liquid is reduced to 1/4 cup, 2 to 3 minutes. Stir in any accumulated juices from the steaks.
Season the steaks with salt and transfer to individual plates. Spoon the pan sauce on top and serve.