Preheat the oven to 400 degrees F.
Season the portobellos with salt and pepper. Place the mushrooms in a small glass baking dish. Pour the wine over the mushrooms. Cover the dish with plastic wrap and refrigerate overnight.
Season the meat with 1 tablespoon of olive oil, salt and pepper. In a hot saute pan, sear the tenderloin for 2 minutes on all sides. Place the pan in the oven and roast for about 6 to 8 minutes for medium rare. Remove from the oven and cool completely.
Remove the portobellos from the refrigerator and drain. In a large saute pan, heat the remaining olive oil. When the pan is hot, add the mushroom caps and cook for 2 minutes on each side. Remove the mushrooms from the pan and cool.
Slice the mushrooms 1/4-inch thick. Slice the tenderloin 1/4-inch thick. Spread both sides of the onion rolls with the aioli. To build the sandwich, place a fourth of the tenderloin on one half of each roll. Top the beef with a layer of the mushrooms and cheese. In a mixing bowl, toss the lettuce with a drizzle of the extra virgin olive oil. Season with salt and pepper. Pile the seasoned lettuce on top of the cheese. Top the sandwiches with the remaining halves of bread. Serve the sandwiches with the sweet potato chips.
Combine the garlic, egg, lemon juice, parsley, salt, and pepper in a food processor or blender and puree. Add the oil in a slow stream and continue to process until the mixture has formed a thick emulsion.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.