Heat up some oil, about 1 tablespoon, in a large nonstick frying pan or griddle over medium heat. Add the slices of onions and season with salt and black pepper to taste.

Cook the onion slices, pressing down with a spatula intermittently, until the onions become softened and caramelized, about 7 to 9 minutes.

Carefully, flip the onion slices, season with salt and black pepper to taste, and cook while pressing down with a spatula intermittently to caramelized, about 6 to 8 minutes or longer as needed.

Carefully transfer the onion slices to a large plate and set aside.

Heat up some oil, about 1 1/2 to 2 teaspoons, in the same pan used to cook the onions under medium high heat.

In batches of 1 to 2 patties, add the smashed patties into the pan. Generously season with salt and black pepper and spread a teaspoon of mustard over the top of each patty.

Cook the patties for 1 to 2 minutes and flip. Season patties with salt and black pepper and cook for an additional 1 to 2 minutes or until desired doneness.

Add a slice of cheese over the cooked patties to melt, about 1 minute. Next, place one cheese patty over the other to form a double cheese patty. Transfer to a plate and repeat process with remaining smashed patties and cheese.

On a plate or serving platter, place down a caramelized onion slice, top with one of the stacked double cheese patties, and place a caramelized onion slice on top to form a burger. Repeat with remaining patties and onion slices for a total of (2) Flying Dutchman burgers.