Easy, Delicious, Korean Street Toast (POV Cooking)

Korean street toast. I feel like my algorithm has been feeding me vids of street vendors making these on their giant griddles for years.
Now that I've got my own I thought I'd make it for myself. Another straightforward and delicious crowd pleaser. Would eat this any time of day. Had a bunch of leftover cabbage and eggs from the okonomiyaki I made earlier and this shares some ingredients.

I encourage you to check out other recipes too and figure out what you like. Some channels I watched to learn mine were Maangchi and Foodwishes.

For my simple approximation of it, which serves about 4 people:

4 cups of cabbage,
a couple handfuls of shredded carrot,
one bunch of green onions
and 4-5 eggs.
Mix together and season with some salt. You want the vegetables to be coated in egg but not swimming in it.

Cook the egg and veggie mix in a buttered pan, while toasting some bread on the side in a pan with butter.

Get both sides toasted and put cheese on one side.

Mix together and season with some salt. Cook the omelete in a buttered pan, while toasting some bread on the side in a pan with butter.
Get both sides toasted and put cheese on one side.

Cut the omelete into an appropriate square shape to fit the bread, trimmings make for a great breakfast wrap later.

Give some ham a quick warming in the pan and stack it with the omelete over the cheese and then dress with mayo, ketchup, and a dusting of white sugar. I also added some miso gochujang sauce over top for some kick.

This makes for such a satisfying breakfast, lunch, or dinner in my opinion. Great for entertaining or just switching things up on your usual ham and cheese sandwich.