Shape four 4-cm (1 ½-inch) thick patties with the ground meat. Season with salt and pepper. Set aside.
In a skillet, brown the buns on both sides in the butter. Keep warm.
In the same skillet, brown the mushrooms in half the olive oil. Season with salt and pepper. Set aside in a warm bowl.
In the same skillet, grill the patties in the remaining olive oil for 5 to 6 minutes per side or until cooked through. Add oil, if needed. Season with salt and pepper. Before the end of cooking, top with the cheese and let melt.
Spread the aioli on the buns. Top the bottom bun halves with the lettuce and add the patties. Add the mushrooms and basil. Sprinkle with a few drops of truffle oil. Cover with the top bun halves.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.