01 - Pat the chopped kimchi dry with paper towels to minimize excess moisture. If desired, mix the kimchi with gochujang and green onion for extra flavor.
02 - Lay out the bread slices on a work surface. Butter one side of each slice evenly.
03 - Flip the bread so the unbuttered side is facing up. Place 1 slice of cheddar and 1 slice of mozzarella on two of the slices. Evenly distribute the chopped kimchi over the cheese, then top each with the remaining cheddar slices.
04 - Close the sandwiches with the other two bread slices, buttered side facing out.
05 - Heat a nonstick skillet or griddle over medium-low heat. Place the sandwiches in the pan and cook for 3–4 minutes per side, pressing gently with a spatula, until golden brown and the cheese is melted.
06 - Remove from heat, let rest for 1 minute, then slice and serve hot.