01 - Pat the chopped kimchi dry with paper towels to remove excess moisture. For enhanced flavor, mix kimchi with gochujang and chopped green onion if using.
02 - Lay out bread slices on a clean work surface. Spread softened butter evenly on one side of each slice.
03 - Flip bread slices so unbuttered side faces up. Place one slice cheddar and one slice mozzarella on two of the bread slices.
04 - Distribute prepared kimchi evenly over the cheese layer, then top each with remaining cheddar slices.
05 - Complete sandwiches by placing remaining bread slices on top, buttered side facing outward.
06 - Heat nonstick skillet or griddle over medium-low heat. Cook sandwiches for 3–4 minutes per side, pressing gently with spatula, until golden brown and cheese is thoroughly melted.
07 - Remove sandwiches from heat and let rest for 1 minute. Slice diagonally and serve immediately while hot.