Mix the mayonnaise, ketchup, relish, onion, vinegar and salt in a small bowl, then cover and refrigerate prior to serving.
Preheat a large, non-stick pan over medium heat for 2-3 minutes. Add 1 tablespoon of oil to the pan, tilting and rotating the pan to distribute the oil evenly. Add the buns in batches, toasting for 1-2 minutes on one side only, until they develop golden brown edges. Transfer to a cutting board and set aside.
In the same hot pan, add the remaining oil and then the burgers. Sear for 4-5 minutes on each side, until lightly browned, then turn off the heat and keep warm in the pan.
To assemble the Big MacFry Burger, start from the bottom up, on the cutting board. On the first bun, add a tablespoon of the sauce, some red onion slices and shredded lettuce. Next place a burger patty, followed by a slice of cheese and some pickles, then a bun. To complete this double decker burger, on top of the second bun, repeat by adding the sauce, onion, lettuce, burger, cheese and pickles, followed by the third and final bun.