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Form the ground chuck into 8 equal balls, and then into patties. Top four patties with some of the pastrami and a slice of cheese. Top with the remaining patties, and press the edges to seal in the filling. Reshape the burgers if necessary so they are of an even thickness.
Just before grilling, season the patties with Traeger Prime Rib Rub.
When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Arrange the burgers on the grill grate and smoke for 30 minutes.
Increase the temperature to 300 and continue to cook until the internal temperature of the burgers reaches 165F, about 30 minutes. (Put the temperature probe into the burgers from the side, not the top, for an accurate reading.)
To serve, spread the cut sides of the buns with thousand island dressing. Put a burger on the bottom half of each bun, and top with sauerkraut, if desired. Serve immediately.