Heat oil in a nonstick pan, add the onions and a pinch of salt. Cook on medium flame, stirring occasionally, until the onions are lightly browned and caramelized, about 20 minutes. Turn off the heat and let the onions cool slightly.
In the meantime combine mayonnaise and sour cream in a mixing bowl. Add the cooled onions, everything bagel topping, salt and pepper. Mix well and refrigerate for at least 1 hour for the flavors to meld.