Shred the cabbage and carrots to prepare.
In a bowl, mix the shredded cabbage, carrots, 2 eggs, salt, and pepper.
Heat butter in a pan and make an egg patty (medium heat).
Remove the egg patty, reheat butter, and toast two slices of bread (medium heat).
Cut the egg patty to fit the bread size, sprinkle sugar and ketchup, then assemble the sandwich.