Pat chops dry and season with salt and pepper. Heat oil in a skillet and brown chops for 2 minutes per side in two batches.
Put potatoes in the bottom of a 6-quart slow cooker. Toss sauerkraut and onion together over them, then arrange browned chops on top.
Whisk beer, broth, mustard and caraway and pour around the pork. Cover and cook on low for 6 hours until the potatoes and chops are fork-tender; pork must reach at least 145°F, with marbled blade chops often near 190°F when tender.
Lift chops carefully with two wide utensils and rest for at least 3 minutes. Stir the potatoes and sauerkraut gently through the cooking juices.
Serve each chop with a share of potatoes, sauerkraut and a small spoonful of the hot liquid.