This showstopper of a roast is actually very easy to make. Look for a center-cut piece of tenderloin with an even thickness so it cooks properly. Simply sear and roast it to medium-rare, then enjoy the compliments that are guaranteed to follow.
Heat a large ovenproof skillet over medium-high heat. Pat the beef dry and season all over with salt and a generous amount of pepper. Add the oil to the skillet and heat until shimmering. Add 1 tablespoon of the butter and swirl to melt. Add the beef and sear until mahogany brown on all sides, about 8 minutes total.
Transfer the skillet to the oven. Roast until an instant-read thermometer inserted in the center registers 125 degrees F for medium-rare, about 25 minutes.
Meanwhile make the ragout: Heat 2 tablespoons of the butter in a large skillet over medium-high heat. Add the mushrooms and spread them out evenly; increase the heat to high. Let the mushrooms cook, undisturbed, until browned, then shake the skillet to flip them over. Add the additional butter along the sides of the skillet as the mushrooms cook, if the skillet seems very dry. Continue to cook until nicely browned, about 5 minutes.
Add the shallot and cook, stirring often, until softened, about 2 minutes. Season the mushrooms with 1/2 teaspoon salt and some ground black pepper; add the thyme. Pull the skillet off the heat and add the Madeira. Return the skillet to the heat and scrape up any of the brown bits from the bottom with a wooden spoon. Add the heavy cream and bring to a boil. Remove from the heat and keep warm.
When the beef is ready, transfer to a cutting board, tent very loosely with aluminum foil, and let rest for 10 to 15 minutes.
Slice the beef across the grain crosswise, arrange on a platter and serve with the mushroom ragout.