Preheat the oven to 375 degrees and lightly grease an 8x8 inch baking dish.
Melt the butter in a saucepan over medium heat. Whisk in the flour and cook for one minute.
Slowly whisk in the milk. Add the salt, black pepper, and paprika. Continue whisking until the sauce thickens slightly.
Remove the sauce from the heat and stir in 1 1/2 cups of the cheddar cheese until melted.
Spread one third of the potato slices in the baking dish. Top with half the ham and one third of the cheese sauce.
Repeat the layers with another third of the potatoes, the remaining ham, and another third of the sauce.
Finish with the last third of the potatoes and the remaining sauce. Sprinkle the rest of the cheddar cheese over the top and dust with paprika.
Cover with foil and bake for 45 minutes. Remove the foil and bake 15 minutes more until the potatoes are tender and the top is golden.