Combine all ingredients for the aioli in a mixing bowl. Whisk together and set aside.

Light griddle and set to medium high heat. Place a large cast iron skillet on the griddle surface and preheat griddle and skillet for 10 minutes.

Add butter into the cast iron skillet and let it melt. Once melted, add sliced onions and allow them to cook down and caramelize for 30 minutes, stirring often.

When onions have been cooking for about 15 minutes, add bacon to the griddle and cook to desired doneness. When bacon is halfway done, flip it and add beef patties to the griddle.

Cook beef patties for two minutes before flipping. Add two slices of cheese to each patty and allow it to melt while cooking the patty for an additional two minutes, four minutes total. Remove the patties and bacon from the griddle, and the onions from the skillet.

Add the bread, butter side down, to the griddle and allow it to brown on one side. About one minute.

Remove the bread, and place two slices browned side down on a cutting board. Apply aioli dressing, and top with two burger patties, bacon, caramelized onions, and additional aioli dressing. Top with remaining two pieces of bread, slice in half and serve hot.