Season the meat with the salt and pepper and mix lightly with a fork.
Divide the meat into 4 1/4 pound patties. Put two slices of cheese on two of the patties.
Cover the patties with the other patties and seal with a fork. Form them into oval steaks. Set them aside.
Put the butter into a shallow saute pan and heat to medium. When the butter is melted, add the shallots. Add the sliced mushrooms and saute them until they have browned a little. Add the sherry and keep sauteing the mushrooms until they are a nice brown and caramel color. Add the worcestershire and stir. Set aside.
Heat the grill until it is smoking. Brush it with oil. Open the windows! Put the steaks on the grill and let them sit, undisturbed for 5 minutes. Come back and flip the steaks. Put a few pieces of the remaining cheese on each steak. Check that they are done at the three-minute mark. They are rare at 130°F / 54.44°C
Plate the steaks and put the mushrooms and pan sauce over them.
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