Egg mixture: in a bowl, add in the eggs, cabbage, carrot, onion, salt and pepper, and mix well until combined.
Toast your bread slices in butter until nice and toasty. Set aside
Cook your ham/bacon until crispy, set aside
Pour half of the egg mixture into a pan with butter on medium heat. With a spatula, shape it into a square before the egg sets. Cook for 2-3 minutes or until golden then flip. Cook for another 2-3 minutes or until golden. Repeat with the other half.
Assemble: Place an egg patty onto a sandwich slice, top with a tbsp of sugar, cheese, ham/bacon, ketchup and mayo. Close the sandwich with another slice of bread. Enjoy