1. Preheat the oven to 350°F (175°C) and grease a 2-quart casserole dish.
2. Layer half of the sliced potatoes, diced ham, and chopped onions in the prepared casserole dish. Repeat the layers with the remaining halves of the ingredients.
3. In a saucepan, melt the butter over medium heat. Stir in the flour and cook for about a minute until the mixture is smooth and bubbly.
4. Gradually add the milk to the butter-flour mixture, stirring constantly until the sauce thickens and becomes smooth.
5. Season the sauce with salt, pepper, and paprika, stirring to combine.
6. Remove the sauce from heat and stir in the shredded cheddar cheese until it melts and is fully incorporated into the sauce.
