Preheat your oven to 350*F.  Melt the butter in a large skillet.  Once it begins to foam add the onion and the ham.  Cook, stirring frequently until the oven is softened without allowing it to brown.  Add the drained and rinsed sauerkraut. Sprinkle with paprika and mix well together.

Place half of the sliced potatoes in a buttered 9-inch casserole dish. Season with some salt and black pepper. Spread the ham/sauerkraut mixture over top. Cover with the remaining potatoes. Season lightly.  

Beat the eggs and milk together. Pour this over the casserole. Use the tip of a knife to move things a tiny bit so that it gets right down to the bottom. 

Sprinkle the grated cheese over top.

Bake in the preheated oven for 25 to 30 minutes until heated through, the eggs are set and the cheese is bubbling. Serve hot!