Preheat the oven to 350ºF (180ºC). Have a 9 x 13-inch (23 x 33 cm) baking dish ready.
Set a large skillet over medium to medium-low heat. Add the oil and swirl to coat. Place the sausages in the skillet and cook until golden brown on both sides.
Transfer the sausages to a cutting board. Using a sharp knife, carefully slice them lengthwise down the middle. It is fine if they are not fully cooked through at this stage.
Spread the sauerkraut and its juices into the prepared baking dish. Arrange the halved sausages evenly over top.
Bake for 50 to 60 minutes, until the sauerkraut is heated through and lightly browned around the edges and the sausages are cooked through. Serve hot with skin-on boiled new potatoes and mustard pickles.
Notes
Brown the sausages slowly over medium to medium-low heat so they develop colour without splitting.
The sauerkraut will release liquid as it bakes. It's good stuff for spooning over your potatoes!
Storage
Refrigerate leftovers in a sealed container for up to 4 days. Reheat in the oven or on the stovetop until warmed through.