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When ready to cook, start the Traeger on Smoke with the lid open until a fire is established (4-5 minutes).
Season the burger patties liberally with Beef Shake and place on the grill grate. Close the lid and smoke the burgers for at least 30 minutes. Remove the burgers to a separate plate, turn the temperature setting to High and allow the grill to preheat, lid closed, for 10 minutes.
Return the hamburger patties to the grill, along with the pineapple. Grill for 6-8 minutes. Mop the top of the patties with Teriyaki sauce.
Flip the patties and pineapple. Mop the other side of the patties with a coat of teriyaki sauce. Place the ham on the grill in 8 small piles of 3 slices each.
Grill the burgers for an additional 6-8 minutes, or until an internal thermometer reads 175 degrees F. Top each hamburger patty with a slice of pineapple, a pile of ham, and finally a slice of cheese.
Close the lid and cook for an additional 1-2 minutes to melt the cheese. Buttered buns may be added to the grill at this time, if desired.
Remove burgers from grill, add to toasted buns, and top with additional teriyaki sauce, if desired, and any additional toppings. Enjoy!