In a large sauté pan, on medium heat, add the olive oil, butter, salt, and pepper. Allow the butter and oil to heat up. When the butter has melted, swirl the pan around to ensure the ingredients are combined.
Add the onions and mushrooms. Stir and sauté until the onions are caramelized and the mushrooms have taken on a deep brown colour.
Add the garlic and green pepper. Stir and continue to sauté until the green peppers have lost their colour and have totally cooked into the mixture.
Add the soy sauce and the Worcestershire sauce and stir well.
Continue to sauté on medium heat until the liquid has thickened.
In the meantime, slice the buns lengthwise, leaving one side of each bun connected. Push the bun open and lightly butter each side.
Place the buns on a baking sheet cut side up. Place under the broiler until a light golden crust has been achieved.
Remove the buns from the oven. Split the mushroom mixture equally between the two. Pile the mixture high on the bottom half only.
Top the mushroom mixture with the cheese and return the sandwich to the broiler.
Keep a close eye on the cheese - since everything is already cooked, you will just want the cheese to be melted - not bubbly or browned.