Shred the cabbage thinly.
In a bowl, mix eggs, cheese, salt, and pepper well.
Add the shredded cabbage to the batter and mix evenly.
Add oil to a pan.
Spread the batter evenly in the pan and cook over medium-low heat.
When the bottom is cooked, flip it and cook the other side.
Top with extra cheese, cover with a lid, and cook until the cheese melts.
Serve with ketchup or tomato sauce as desired.