This unusual toasted egg sandwich is packed with cabbage, carrot, and green onion cooked in an egg batter, then layered with ham and cheese in between toasted bread.
Shred cabbage and carrot very thinly using a vegetable peeler.
Beat eggs in a large mixing bowl and add the cabbage, carrot, green onion, and salt; mix well.
Melt butter on a skillet. Spoon in a portion of egg and vegetable mixture and spread it around to about the size of your sandwich bread.
Cook the egg omelettes until golden brown and flip. Transfer the omelette to a plate and repeat the next batch.
Heat ham slices briefly, about 30-60 seconds; set aside.
Toast the sandwich bread in the remaining butter until golden and crisp.
Assemble the sandwich; lay egg omelet, sugar, ketchup, ham slice, cheese slice in between the toasted bread.
Eat this buttery Korean toast right away while they are hot to enjoy all the goodness.