Place the filets on a board and pat them dry with paper towels. Sprinkle the filets with salt and then press the black pepper evenly on both sides. Allow to rest at room temperature for 15 minutes.
Heat 1 1/2 tablespoons of the butter and the oil in a large saute pan over medium-high heat until the butter almost smokes. Place the steaks in the pan and lower the heat to medium. Saute the steaks for 4 minutes on one side and then for 3 minutes on the other side, for medium rare. Remove the steaks to a serving platter and cover tightly with aluminum foil.
Meanwhile, pour all but 1 tablespoon of fat from the saute pan. Add the shallots and cook over medium heat for 2 minutes. Add the beef broth and cook over high heat for 4 to 6 minutes, until reduced by half, scraping the brown bits from the bottom of the pan. Add the Cognac and cook for 2 more minutes. Off the heat, swirl in the remaining 2 tablespoons of butter and 1/2 teaspoon salt. Serve the steaks hot with the sauce poured on top.