Preheat oven to 400°F.
Preheat a large, cast-iron skillet over medium-high heat.
In a large bowl, combine potatoes with a liberal drizzle of EVOO, enough to coat potatoes. Season with salt, pepper, a little nutmeg and caraway seeds. Add to hot pan, toss around and situate in fairly even layer. Transfer to oven and roast about 20-25 minutes.
Rinse and drain sauerkraut.
Combine ketchup, sour cream and relish in a bowl. Season with salt and pepper.
Remove skillet from oven and top the potatoes with sauerkraut, sauce, chopped corned beef and cheese. Return skillet to oven and bake 10-12 minutes more until cheese is bubbly. Serve from hot skillet.