Pass the cooked potatoes and sausages alternately through a meat grinder. Mix together with oatmeal, 1 egg, salt, pepper, nutmeg, caraway seeds, and marjoram. Let rest for 15 minutes. Shape the mixture into 10 patties.
Heat clarified butter in a non-stick pan over medium-high heat. Fry the patties until golden brown on both sides (about 4-5 minutes per side), turning carefully as they are delicate, and reduce heat to medium if needed. Meanwhile, in a separate non-stick pan, heat some clarified butter over medium heat and fry the 5 eggs until the whites are set.
Mix the sour cream with the fresh basil and season with salt and pepper.
Place the bratwurst patties on a plate, add a fried egg on top, drizzle with the basil sour cream sauce, and serve with potato salad.