Place a baking sheet in the oven and preheat oven to 250°F
In small bowl whisk together all ingredients for dressing. Set aside.
Preheat a griddle or large non-stick frying pan over medium low heat. Place the corned beef in pan and lightly heat through. Corned beef will get curly. Remove from pan and lightly pat dry with paper towels to remove moisture.
Butter all 8 slices of rye bread.
Turn 4 slices over and spread with desired amount of dressing, then top with 1 slice of cheese, about 80-100 g of corned beef and a few tablespoons of kimchi then another slice of cheese. Lightly press down to compress the sandwich a bit.
Spread the remaining slices of buttered bread with the dressing and place on top of sandwich, buttered side up.
Add a pat of butter to pre-heated griddle and place as many sandwiches in pan that will fit. Pressing down with a spatula until crisp and golden on bottom (about 3-4 minutes). Flip the sandwiches over and cook until golden and crisp on other side and cheese is melting.
Keep the sandwiches on the warmed baking sheet in the oven to keep warm while you cook the remaining sandwiches.