With a small amount of olive oil heated on medium high, saute mushrooms and onions until soft. Stir in peppers. Place in a bowl and keep warm.
Divide shaved beef into two portions and shape generally into same shape as grinder roll.
Meanwhile toast grinder rolls.
In same skillet as mushrooms were cooked heat a little more olive oil. Place two meat portions in hot skillet and brown. Flip over and immediately place cheese on each meat portion. Heat until cheese is melted.
Using spatula remove meat from skillet and place cheese side down in grinder rolls. Top with mushroom, onion, and pepper mixture.