Step 1

Place 2 bread slices on a work surface. Evenly spread ½ Tbsp. butter over each slice. Turn 1 slice over and spread 2 tsp. gochujang over, then top with ½ cup cheese and half the kimchi. Close sandwich with buttered sides facing out. Sprinkle 2 Tbsp. cheese over top of sandwich, gently pressing to adhere cheese to butter.

Step 2

Heat ½ Tbsp. butter in a medium nonstick skillet over medium-low until foaming. Cook sandwich, cheese side down (if some cheese falls out, use a heatproof spatula to nudge it back underneath the sandwich), gently pressing occasionally with a heatproof spatula, until underside is golden brown and crisp, about 3 minutes. Sprinkle another 2 Tbsp. cheese over top of sandwich, pressing with spatula to adhere. Turn sandwich over and cook until golden brown on second side and cheese inside is fully melted, about 3 minutes. Transfer sandwich to a plate. Wipe out skillet and repeat process with remaining ingredients to make 1 more sandwich.