Mix cabbage, carrot, onion, salt, pepper, cayenne in about in a bowl. Mix until soft.Mix in eggs Melt butter in a skillet. Grill bread on both sides until crispy. Set aside.
Cook Cabbage mix in 1 tablespoon butter. Keep scraping and folding in edges. (Scramble) until egg starts to hold together. Then shape in a rectangle. Cut into 2 equal squares. Cook until brown on both sides.
Place both egg patties on bread. Sprinkle with sugar. The sugar is apparently a necessary element for flavor. Reviewers said to not leave this out.
Place Ham in skillet. Sizzle and flip. Top with cheese.
Place ham on the egg.
Top with ketchup and mayo. According to reviewers this is an essential combo for this dish.