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.