01 - Spread unsalted butter evenly on one side of each bread slice.
02 - Combine gochujang and mayonnaise in a small mixing bowl (if using), then spread the mixture on the unbuttered side of two bread slices.
03 - Place 2 slices of sharp cheddar and 1 slice of mozzarella on the unbuttered side of each prepared bread slice.
04 - Scatter chopped kimchi evenly over the cheese, and top with sliced scallions if desired.
05 - Top the fillings with the remaining bread slices, ensuring the buttered side is facing out.
06 - Heat a nonstick skillet or griddle over medium-low. Place sandwiches in the pan and grill for 3 to 4 minutes per side, pressing lightly, until the bread is golden brown and the cheese is fully melted.
07 - Remove sandwiches from heat. Let rest briefly, then slice and serve hot.