Preheat oven to 375˚F. Use a bit of the butter to grease an 8-inch square baking dish, and place a pot of lightly salted water on to boil. In a small bowl, whisk together the eggs, salt, mustard, white pepper, and milk and set aside. When the water is boiling, add the macaroni, stir to keep from sticking, and cook until barely tender. Drain into a colander and cool under running water.

Combine the cubes of mild and sharp cheddar. Place a layer of the macaroni on the bottom of the dish, scatter a layer of cheese cubes over it. Continue making layers until all the macaroni and cheese have been used. Pour the egg and milk mixture over the layers and jiggle pan to distribute evenly. Combine the bread crumbs and the paprika and sprinkle evenly over the top, then dot with thin slices of the remaining butter. Bake until brown and bubble, about 20 minutes.