With the rack in the middle position, preheat the oven’s broiler.
In a large non-stick skillet over high heat, brown the meat in the oil, breaking it up with a wooden spoon. Season with salt and pepper. Set aside on a plate.
In the same skillet, brown the mushrooms and onion. Add oil, if needed. Season with salt and pepper. Return the meat to the skillet. Add the broth and sauce and stir to combine. Adjust the seasoning. Sprinkle with the cheese and let it melt. Remove the skillet from the heat.
Open the buns and place them flat on a baking sheet. Toast the buns in the oven on each side.
Place each bun on a plate. Garnish with lettuce and cover with the meat mixture. Drizzle with the pan juices.
If you have only a few slices of fondue meat, scale back the recipe into a quarter to prepare a single sub.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.