Heat a large skillet over medium-high heat and stir in the ground beef and onion. Cook and stir until the beef is crumbly, evenly browned, and no longer pink. Drain and discard any excess grease. Stir in the relish.
Spread processed cheese sauce on each bun half, place a scoop of the meat mixture between the halves. Wrap each sandwich in foil and refrigerate or freeze until needed. Bake in an oven preheated to 350 degrees F (175 degrees C) until hot, 5 to 10 minutes if refrigerated, 20 minutes if frozen.