To make the patties, combine all the ingredients in a bowl and mix very well with your hand. When it is properly emulsified, divide the mixture into four equal-sized balls and form into thin patties.

Mix all the ingredients for the sauce together in a small bowl and set aside until assembling the sandwich.

Fry your patties in a little oil over medium-high heat. When they are golden brown on on side, flip them over. Add a slice of cheese on top of each patty; add the maple syrup to the pan, and let the maple syrup reduce and glaze the bottom of the patties. Make sure the syrup does not burn.

To assemble, put a tablespoon worth of sauce on the bottom of the bun, add your patty, and top with an egg. Cover the sandwich with the top of the bun and eat immediately.