Shred cabbage and carrot and prepare them.
In a bowl, mix shredded cabbage, carrot, 2 eggs, salt, and pepper.
Heat olive oil in a pan and make an egg patty (medium heat).
Take out the egg patty, melt butter in the pan, and toast two slices of bread (medium heat).
Cut the egg patty to fit the bread size, sprinkle sugar and ketchup, and assemble the sandwich.