For the aioli:In a bowl, add the mayonnaise. Puree garlic by using a mortar and pestle or you can mince garlic and then mash with the side of knife on a cutting board. Moving back an forth until mashed into a puree. Add the puree to the mayonnaise. stir well to combine. Add the chopped egg white and season with pepper. Stir to combine.For the sandwich:Lay out the pancetta on a greased, foil lined sheet pan. Cook the bacon in a 375 degree F oven until crisp. Turning once to cook evenly. About 15 minutes.Slice tomatoes and avocado. Lightly toast bread.Spread a layer of egg aioli onto bottom slice of sandwich toast. Top with lettuce, bacon, tomato, avocado and then basil leaves. Top with other slice of toasted bread. Hold together with sandwich picks. Slice each sandwich in half and serve immediately.Enjoy!