Pat chops dry; add salt and pepper. Heat oil in skillet; brown in two batches 2 minutes per side.
Put potatoes in bottom of 6-quart slow cooker. Toss sauerkraut and onion over them; top with browned chops.
Whisk beer, broth, mustard, and caraway; pour around pork. Cover; cook on low 6 hours until potatoes and chops fork-tender. Pork must reach at least 145°F; marbled blade chops often reach 190°F when tender.
Carefully lift chops with two wide utensils; rest at least 3 minutes. Gently stir potatoes and sauerkraut through juices.
Serve each chop with potatoes, sauerkraut, and small spoonful hot liquid.