Thinly slice the cabbage.
Slice carrots and cucumber thinly.
Beat the eggs and cook in a frying pan to make an omelet, then cut into thin strips.
Heat oil in a pan and stir-fry the cabbage and carrots.
Season the stir-fried vegetables with salt and pepper.
In a bowl, mix the stir-fried vegetables, egg strips, mayonnaise, mustard, salt, and pepper to make the sauce.
Prepare as a filling for gimbap.