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