(This steak is twice what I need, so freezing half of it.)
Dice the onion and mushrooms. The smaller mushroom pieces get more evenly distributed than sliced. Slice the steak, against the grain, into thin slices.

Lightly butter both sides of the buns. Toast on both sides in a skillet over medium heat to desired brownness. Remove from skillet and set aside.

Over medium-high heat, dry skillet, cook the mushrooms, stirring frequently, until most of their moisture evaporates. Stir in a pat or two of butter and continue cooking until browned. Remove from skillet and set aside.

Add 1-2 T. oil to the skillet. Cook the onions over medium-high heat, stirring frequently, until soft and browned, about 8-10 minutes. Set them aside with the cooked mushrooms.

If desired, spread a little mayonnaise in the buns. Fold sliced cheese in half and place in toasted buns. Pile in the steak mixture. Serve hot and enjoy!