Crack eggs in a bowl and beat for a few seconds. Add cabbage, carrots, onions and onion leeks. Season with salt and pepper and mix until all ingredients are well combined.
Preheat pan on medium low heat. Add cooking oil and pour in egg mixture. Cook for a few minutes until egg is no longer too runny to flip and cook the other side. Remove egg and set aside.
Optional: add a little oil to cook ham for a few minutes on both sides. Remove from pan.
Spread butter or mayonnaise on bread and toast using the same pan (on low heat) until golden brown. Turn off heat.
Add 1/4 of a teaspoon of sugar on top of toasted bread. Add/squirt on about a tablespoon of mayonnaise and a teaspoon ketchup (or according to taste). Cut cooked egg into square shapes to fit bread. Assemble on top of the bread with mayo and ketchup. Add half a teaspoon of sugar. Optional: add ham and sliced cheese. Put the other slice of bread on top and cut diagonally. Serve while hot.
