1. In a large nonreactive skillet, bring 1 cup of water to a boil. Add the asparagus tips and boil over high heat until just tender, about 3 minutes. Drain in a colander and rinse under cold water to refresh.
2. Season the steaks with salt and pepper. Heat the oil in the skillet over moderately high heat until almost smoking. Add 1/2 tablespoon of the butter and when the foam subsides, add the steaks and cook, turning once, until well browned, about 6 minutes for medium-rare.
3. Remove the skillet from the heat and pour in the Cognac; stand back in case it ignites. Return the skillet to moderately high heat and turn the steaks to coat. Cook until the sauce is slightly reduced, about 2 minutes. Transfer the steaks to a plate.4. Melt 1/2 tablespoon of the butter in the skillet. Add the mushrooms and sauté over moderately high heat, stirring occasionally, until browned and tender, about 6 minutes. Add 1 tablespoon butter and the shallots and cook over moderate heat, stirring, until the shallots soften, about 4 minutes. Increase the heat to moderately high and add the asparagus tips. Pour in the Madeira and boil until reduced by one-third, about 2 minutes. Season with salt and pepper. Stir in the mustard and the remaining 1/2 tablespoon butter.
5. Reduce the heat to moderate and add the steaks. Turn to coat with sauce and simmer to heat through, about 1 minute. Transfer the steaks to plates, spoon sauce and vegetables on top and serve.
Serve With: Orzo or egg noodles.