Spread asparagus on small baking sheet and dress with a liberal drizzle of extra-virgin olive oil and season with salt. Roast the spears in a hot oven until tender and ends are crisp and slightly brown at edges, about 10 to 12 minutes. Asparagus should remain bright green.
Take the chill off the meat then pour the black pepper onto a small plate. Heat the extra-virgin olive oil in a nonstick skillet over medium-high to high heat. When oil smokes, press each steak into pepper to coat then place peppered side down in the skillet. Sear and caramelize the meat 3 to 4 minutes, turn and cook 2 minutes more for rare, 3 minutes for pink.
While the meat cooks, heat a small skillet over medium flame and melt then butter. Add mushrooms and lightly saute them for 4 to 5 minutes. Season the mushrooms with salt and pepper and add cognac or brandy to the pan. Be careful of flare ups. You may want to add the liquor off the stove top then return the skillet to the heat. Reduce the liquid by half, cooking off the alcohol and concentrating the flavor, then stir in the cream and warm it through. Reduce heat a bit and let sauce thicken 2 to 3 minutes.
Spoon sauce over meat and serve with asparagus alongside.