01 - Pat the chopped kimchi dry with paper towels to remove excess moisture. If desired, mix the kimchi with gochujang and chopped green onion for additional flavor.
02 - Lay out all bread slices on a clean work surface. Spread softened butter evenly on one side of each slice.
03 - Flip the bread so the unbuttered side faces up. Place 1 slice of cheddar and 1 slice of mozzarella on two of the bread slices. Distribute the chopped kimchi evenly over the cheese, then top each with another cheddar slice.
04 - Complete each sandwich by placing the remaining bread slices on top, buttered side facing outward.
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 cheese is fully melted.
06 - Remove sandwiches from heat and let rest for 1 minute. Slice diagonally and serve hot.