Heat the oil in a large skillet over medium-high heat and brown the bratwurst on two sides, about 5 minutes total; they will not be cooked through.
Spread the potatoes and onion in a 6-quart slow cooker and cover them with the sauerkraut.
Whisk the cider, mustard, caraway and pepper and pour the mixture into the cooker.
Set the browned bratwurst over the sauerkraut and arrange the apple wedges on top.
Cover and cook on low until the potatoes are tender and the sausages reach 160°F, 4 1/2 to 5 hours.
Serve each brat with potatoes, apples, kraut and enough cider liquid to moisten the plate.