Prepare the vegetables by washing and slicing the cabbage thinly, julienning the carrot, and finely chopping the green onions.

In a mixing bowl, whisk together the two eggs, then add the prepared vegetables, salt, and black pepper.

Spread butter on two slices of bread, heat the frying pan, and toast the bread until golden brown.

In the same pan, pour the egg and vegetable mixture in a rectangle shape, and cook until set.

Assemble the toast by placing ketchup on one slice, adding half of the omelette, and top with cheese and the other half of the omelette.

Serve warm, sliced if desired.