When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 400 degrees F and preheat, lid closed, for 10 to 15 minutes.
Wet your hands with cold water and divide the ground chuck into 4 parts. Using a gentle touch, roll each part into a ball, then flatten to a thickness of about 3/4-inch. Rewet your hands as necessary to keep the meat from sticking.
Using your thumbs, make a wide shallow depression in the top of each. (This helps keep the burger an even thickness as it cooks.)
Season with the Traeger Prime Rib Rub and brush the top and bottom of the burgers with canola oil to help get a good sear on the outside.
Arrange the burgers, depression side down, on the grill grate and grill for 10 minutes. Turn with a spatula and continue to grill another 5 to 10 minutes, or until the internal temperature of the burgers is 155 degrees F.
Cheese Sauce: Melt the butter in a small saucepan over medium heat. Whisk in the flour and cook for 1 minute, until slightly golden.Add the milk, increase the heat to high and cook, whisking constantly, until slightly thickened, about 5 minutes. Remove from the heat and whisk in the cheese until melted; add the Parmesan and season with salt and pepper, to taste. Keep warm while the burgers finish cooking.
Toast the buns if desired. Transfer the burgers to the bottom halves of the buns, being careful not to spill any juices that have pooled in the depressions.
Spoon a generous amount of the cheese sauce on top. Serve with your favorite toppings and serve immediately. Enjoy!