In a skillet, add oil and swirl to cook the bottom of the pan. Turn heat to medium-high and add the sliced onions. Cook, stirring occasionally until the onions have softened, but not browned.

Remove the onions from the pan and set aside in a bowl.

Butter one side of each piece of bread and place butter side down into Parmesan cheese. Set aside.

Wipe out the skillet and add the hamburgers. Cook over medium-high heat to desired doneness. Turn off the heat.

Place 2 tablespoons of pub cheese on each burger patty, and place the cooked onions on top of the cheese. Put a lid on the skillet and allow the residual heat to slightly soften the cheese and rewarm the onions.

While waiting for the cheese to soften, heat a separate skillet over medium heat. Once skillet is hot, place bread Parmesan side down in the pan. Cook without turning or disturbing until you can see the edge of the cheese turning light golden.

Carefully remove bread from skillet making sure to get under the cheese, using a quick motion and a sturdy spatula.

Set bread Parmesan side up on 4 separate plates.

Remove lid from skillet and place hamburgers on top of the bread. Serve immediately.