Classic Korean Street Toast (Gilgeori Toast)

In a medium bowl, whisk together the eggs, shredded cabbage, finely diced carrot, sugar, and salt until well combined.

Heat a large non-stick skillet over medium heat. Add 1 tablespoon of butter and melt it, swirling to coat the pan.

Pour half of the egg mixture into the skillet, spreading it into a rectangular shape that roughly matches the size of two slices of bread placed side-by-side. Cook for 2-3 minutes until the edges are set and the bottom is golden brown.

Carefully flip the egg omelet and cook for another 1-2 minutes until cooked through. Remove from the skillet and set aside. Repeat with the remaining egg mixture and 1/2 tablespoon of butter to make a second omelet.

Add the remaining 1/2 tablespoon of butter to the skillet. Place the four slices of bread in the skillet and toast them over medium heat for 1-2 minutes per side, until golden brown and crispy.

To assemble, place one egg omelet on two slices of toasted bread. Fold the omelet to fit the bread, then top with the remaining two slices of toasted bread. Repeat for the second sandwich.

Serve immediately, optionally with a drizzle of ketchup on top.