Begin by thinly slicing the cabbage, julienning the carrots, and chopping the green onions. Set these aside.

In a medium bowl, whisk together the eggs, salt, and pepper. Add the prepared vegetables and mix well.

Heat a frying pan over medium-low heat and melt the butter. Coat both sides of the bread with melted butter and cook until golden brown.

Pour the egg and vegetable mixture in the pan, cooking for about 3-4 minutes until set. Cut into two squares and cook until fully set.

Assemble by placing ketchup on one slice of toast, adding one square of omelette, cheese, and mayonnaise before topping with the second slice.