Heat the oil in a large skillet over medium heat. Add the onion and cook, occasionally stirring, until it is very soft, about 7 minutes.
Stir in the sauerkraut and remove the pan from the heat. While the onions are cooking, make the sauce. Mix the mayonnaise and mustard together in a small bowl.
Form the bratwurst meat into four burger patties. Preheat your grill to medium heat. Once it's hot, cook the bratwurst burger patties until they are fully cooked.