Let's cook.
In a medium bowl, whisk together the eggs, shredded cabbage, diced carrot, diced onion, salt, and black pepper until well combined.
Heat a large non-stick skillet over medium heat. Add 1/2 tablespoon of butter and let it melt.
Pour half of the egg mixture into the skillet, spreading it into a rectangular shape roughly the size of two slices of bread. Cook for 2-3 minutes per side, or until golden brown and cooked through. Remove and set aside. Repeat with the remaining egg mixture and 1/2 tablespoon of butter.
In the same skillet, toast the bread slices over medium heat for 1-2 minutes per side, or until lightly golden.
To assemble, place one slice of toasted bread on a plate. Spread 1/2 tablespoon of ketchup evenly over it.
Place one cooked egg patty on top of the ketchup-covered bread.
Sprinkle 1/2 teaspoon of sugar over the egg patty.
Top with another slice of toasted bread to form a sandwich. Repeat for the second serving.
Serve immediately and enjoy this delicious Korean street food breakfast.
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