Caramelized Onions: Heat the canola oil in a large skillet over medium heat. Add the onions and cook until soft and lightly caramelized about 15 minutes. Add the mustard and a pinch of salt and cook for another 2 minutes. Remove the onions from the pan to a small bowl and set aside.
Special Sauce: In a medium bowl combine all the ingredients and whisk until smooth.
Burgers: Preheat the broiler to low.
Form the ground meat mixture into 6 equal patties. Do not over handle or compress the patties, keep them loose. This will help create a tender burger. Over mixing and compacting will result in a tough heavy burger.
Heat the canola oil a large heavy-bottomed skillet over medium-high heat.
In a small bowl combine the salt, pepper and garlic powder and season the burgers generously with the mixture. Put the patties in the skillet and cook for 4 minutes. Flip and let cook for 1 minute, then top each patty with a piece of cheese. Cook for another 2 minutes until the cheese is melted and the burgers are medium.
While the burgers are cooking, lightly brush the buns with melted butter and put them on a sheet pan. Broil until lightly toasted, about 2 minutes.
To assemble, split the buns and spread each half with about a tablespoon of the special sauce. Put the burgers on the bottom half of each bun, top with caramelized onions, tomato and lettuce. Cover with the top half of the bun and serve.