Prepare the vegetables by finely slicing the green cabbage, dicing the onion, and shredding the carrot. If using garlic chives or scallions, chop them into small pieces.

In a non-stick pan, melt 1 tablespoon of butter over medium heat. Place two slices of bread in the pan and toast for about 1-2 minutes on each side until golden brown.

Mix the prepared vegetables with 1 large egg, adding a pinch of salt and pepper. Whisk until well combined.

Pour the veggie-egg mixture into the heated skillet, spreading it into a round shape. Cook for about 3 minutes until bottom is golden, then flip to cook for an additional 2 minutes.

Place the cooked omelet on one slice of toasted bread. Sprinkle a heaping tablespoon of sugar over it, then drizzle with ketchup. Top with the second slice of bread.

Cut the sandwich in half, serve warm, and enjoy with pickled vegetables or fresh fruit on the side.