In a large bowl, combine the ground beef, diced onion, egg, breadcrumbs, oregano, salt, and pepper.
Mix well and form into 6 large patties or 12 smaller ones. Use the bottom of a saucepan or burger press to flatten evenly.
Set your Traeger (or pellet smoker) to 300°F and allow it to come to temperature in smoke mode.
Place the patties directly on the grill grates. Insert a temperature probe into the thickest patty, if using.
Smoke for about 1.5 hours, or until the internal temperature reaches 145°F.
Mix together the BBQ sauce and Worcestershire sauce.
Baste each patty generously, then top with a slice of cheese.
Continue cooking until the internal temperature reaches 165°F and the cheese is melted.
While the burgers finish cooking, lightly toast your burger buns on the grill for 1–2 minutes.
Spread burger sauce on the top buns.
Layer with lettuce, tomato, pickles, avocado, beetroot, red onion, and the smoked patty.