Let the beef come to closer to room temperature by letting it sit out for 30 minutes.
Then heat your oven to 375 degrees.
Very finely chop the shallot. Either finely chop the garlic or run it through a garlic press.
In a small bowl combine 2 tablespoons of the butter, half of the chopped shallot, the garlic, ½ teaspoon salt, and ½ teaspoon pepper.
Remove the beef from the packaging and pat it dry with a paper towel. If there is butcher's twine wrapped around the beef, leave it. Use your hands to spread the butter mixture all over the beef.
Place the beef on a pan and place it in the oven. After 20 minutes, increase the heat of the oven to broil for about 3-4 minutes, until a crust forms on the beef. Then reduce the temperature to 225 degrees.
After an hour, check the temperature of the beef. For medium rare beef, you want to remove it from the oven at 130 degrees. Let the beef cook longer if necessary. I had a 2.2 pound roast and it cooked in just over 90 minutes total.
While the beef is cooking, start to prepare the gravy. Melt 1 tablespoon of butter in a skillet over medium heat. Add the mushrooms and season with salt and pepper. Toss the mushrooms to evenly coat them in the butter. Be patient and let the mushrooms brown. Then add half of the sherry and the remaining chopped shallot. Stir frequently and let the sherry reduce by half, the reduce the heat to low.
Once the beef has reached 130 degrees, remove it from the oven, place it on a cutting board, and top it with foil. Let it rest for 20 minutes. Take the pan you used to cook the beef, and pour the remaining sherry over the pan drippings. Use a rubber spatula to scrape up any drippings and brown bits, then pour this into a the skillet with the mushrooms.
Melt 2 teaspoons of butter in a small bowl placed in the microwave. Stir in the flour to make a paste. Add this paste and the beef broth to the skillet with the mushrooms. Use the rubber spatula to stir all of the ingredients together. Bring to a slow simmer, and let the gravy thicken. Season it with salt and pepper to taste.
After the beef has rested for 20 minutes, slice it into very thin slices. Serve it with the gravy.