Squeeze excess liquid from kimchi using your hands or a clean kitchen towel. You want it damp but not dripping - too wet and your bread goes soggy. Roughly chop into bite-sized pieces.

In a small bowl, stir together 1 tablespoon softened butter with gochujang and sesame oil. This gets spread on the inside of the bread for a flavor hit in every bite.

Spread the gochujang butter on one side of each bread slice. Flip two slices butter-side down. Divide half the cheddar between them, then pile on the kimchi, then the remaining cheddar. Top with remaining bread, butter-side up.

Heat a large skillet over medium-low heat. Melt 1 tablespoon plain butter in the pan, swirling to coat. Add sandwiches and cook undisturbed for 3-4 minutes until the bottom is deeply golden and crisp. Press gently with a spatula to help everything meld together.

Add remaining 1 tablespoon butter to the pan. Carefully flip sandwiches and cook another 3-4 minutes until the second side is golden and cheese is fully melted. Peek underneath - you want dark golden spots, not pale blonde. Let rest 1 minute before cutting.

Cut sandwiches diagonally and sprinkle with scallions. Serve immediately while the cheese is still stretchy.