Heat a skillet to medium heat.
Place the cheese and the kimchi on one slice of bread. Spread 1 tablespoon of mayonnaise on the outside of the top piece of bread, and place the sandwich mayonnaise side down on the skillet. Cover with the lid of a saucepan. Cook for around 3 minutes.
Spread the remaining 1 tablespoon of mayonnaise on the outside of the top piece of bread, and flip. Cook until golden brown, approximately another 3 minutes.
Remove from heat, and enjoy!