Heat a large skillet over medium-high with a glug of olive oil. Pierce sausages several times and then brown on all sides in skillet, about 10 minutes. Remove and set aside.
Add a little more olive oil and a knob of butter to skillet. Toss in onions, add a pinch of salt, and sauté until lightly browned and starting to soften. If needed, add a little more butter and then the apple slices, toss gently and cook with the onions for a couple of minutes. Lastly, add the potatoes and toss with onion-apple mixture and cook, stirring frequently for a few more minutes. Season lightly with salt.
Add the drained sauerkraut, apple juice and brown sugar, and, if desired, more caraway seed. Stir to combine and bring to a simmer.
Nestle sausages in apple-sauerkraut-potato mixture, cover and simmer for 20-25 minutes, stirring occasionally. Remove lid and simmer another 20-25 minutes until sausage is cooked through, potatoes are tender and most of the liquid has evaporated, stirring occasionally.
Season with salt and pepper and serve, with grainy mustard and rye bread or soft pretzel rolls with butter. Enjoy!