Place the oil in a 10" cast iron or other heavy skillet set over medium-high heat. Add the sausages and brown on all sides, but do cook through. Remove the sausages from the pan and set on a plate.
Drain the fat from the skillet. Add the sauerkraut, onion, carrots, potatoes, rosemary (or sage), pepper and beer (or stock) and stir to combine. Set over medium heat and bring to a simmer. Set the sausages on top. Cover and cook 12 to 15 minutes, or until the sausages and vegetables are cooked.