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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 300 degrees F and preheat, lid closed, for 10 to 15 minutes.
Combine the Traeger Prime Rib Rub and the Italian seasoning in a small bowl. Coat the meat with olive oil. Season with the spice mixture.
With a paring knife, cut small slits in the roast and insert the garlic slices. Put the meat on a rack in a 9- by-13 inch baking pan.
Lay the onion slices in the pan and pour in the beef broth. Roast the meat until the meat reaches a temperature of 145 degrees F, about 2 hours.
If the bouillon seems to be evaporating too quickly, add a little water to it. You do not want the bottom of the pan to dry out as the juices are an important part of the sandwich.
Wrap the meat in plastic wrap and tip the juices into a covered container. Chill in the refrigerator for several hours, preferably overnight.
Thinly slice the roast across the grain, preferably on a meat slicer. Skim any solid fat off the juices. Pour the juices into a skillet and reheat. (You should have at least 3 cups. If not, add a bit more beef broth.)
Using tongs, dip a few slices of meat into the juice and arrange on the hoagie. If you like your sandwich very wet, carefully dip the cut sides of the bread in the juice before topping it with meat.
Add fried peppers and giardiniera, if using. Serve additional juice on the side, if desired.