Preheat the oven to 350 degrees F.
Place the bacon on a baking sheet and bake until crisp, 12 to 15 minutes.
In a bowl, mix together the ground beef, white onions and some salt and pepper until just combined. Don't overwork it. Form the beef into four 1-inch-thick patties and use your thumb to create an indent in the center of each burger. Place on a plate and refrigerate until ready to grill.
Preheat the grill to medium-high heat and brush the grill grates with the oil. Place the burgers on the grill and cook, 3 to 5 minutes per side. Add the cheese slices to the burgers the last minute of grilling, covering the grill to help the cheese to melt. Remove the burgers from the grill to rest. Toast the buns cut-side down for 1 minute when the burgers are resting. Sandwich the burgers with the Vidalia onions, bacon, shredded lettuce, tomatoes, avocado and Jamie's Special Sauce.
Mix the mayonnaise, ketchup and mustard together in a small bowl. Makes 1/2 cup.