In a small bowl, combine cabbage, carrot, scallions, salt and pepper. Mix well and set aside.
In a small bowl, beat the eggs lightly.
In a skillet, heat the butter or margarine over medium heat. Pour in the beaten eggs and cook, stirring occasionally, until scrambled and cooked through, about 2 to 3 minutes. Remove from heat and set aside.
In a large cast-iron or nonstick skillet, toast the bread slices on both sides until golden brown, about 2 to 3 minutes per side.
Transfer the toasted bread to a plate and sprinkle the top of each toast with the cabbage mixture. Top with the scrambled eggs and cheese, if using.
Drizzle with ketchup and mayonnaise, to taste.
