To prepare the burgers, shape the ground beef into even portions, then form them into 4 quarter-pound patties, ensuring the edges are well-sealed. Place the patties on a parchment-lined baking sheet and refrigerate for 1 hour before cooking.
Prepare the grill, when the grill reaches 225°F and clean smoke, season patties with salt and pepper, then place them on the cooler side of the grill to smoke for about 1 to 1.5 hours. Monitor the internal temperature using a digital meat thermometer and adjust air vents for consistent heat.
Caramelize the onions by using a cast iron skillet over indirect heat on the grill or stovetop. Combine onions, oil, and butter in the pan, stirring occasionally. Cook for around 10 minutes until the onions soften and develop golden brown edges.
To sear the burgers, move them to the hot grill side when they're around 10 degrees from your desired temperature, creating a crust. Melt cheddar cheese and toast buns. To serve, place smoked burgers on a platter, then assemble with lettuce, burger patty, caramelized onions, bacon, tomato, ketchup, mustard, and mayo.