01 - Evenly spread softened butter on one side of each bread slice.
02 - In a small bowl, combine gochujang and mayonnaise if using. Spread this mixture on the unbuttered side of two bread slices.
03 - Place 2 slices of sharp cheddar and 1 slice of mozzarella on top of the gochujang-mayo side of each prepared bread slice.
04 - Distribute chopped kimchi over the cheese layer. Sprinkle with scallions if desired.
05 - Top each sandwich with the remaining bread slices, buttered side facing out.
06 - Preheat a nonstick skillet over medium-low heat. Place sandwiches in skillet and grill for 3 to 4 minutes on each side, pressing gently, until bread is golden and the cheese has melted.
07 - Remove sandwiches from heat. Let cool briefly, slice in half, and serve immediately.