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.
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.
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. Melt 1/2 tablespoon of the butter in the skillet.
Add the mushrooms and saut 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.
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.