In a small bowl, add Thousand Island Dressing and sauerkraut. Mix well.
Generously spread butter on one side of each piece of marble rye.
Lay one piece of bread down on a cutting board, buttered side down (You want the butter on the OUTSIDE of the sandwich.)
Spread 1 - 2 tablespoons of mixture onto one piece of bread.
Top with 2 slices cheese, 1/2 of the sauerkraut and all of the meat.
Spread another tablespoon of the dressing over the meat.
Top with remaining cheese.
Spoon 1 - 2 tablespoons of the sauerkraut mixture over cheese and carefully spread to cover.
Top with remaining piece of bread, butter side out, and press firmly to close the sandwich.
Place a heavy-bottomed frying pan over medium heat.
When hot, carefully place the sandwich in the pan. Press down lightly with a spatula. Cook until the bread is crisp and golden brown, about 4 minutes. Watch closely. You want it toasted, not burnt.
Flip. Cook until the second side is golden brown and the cheese has melted, about 4 minutes more.
Cut in 1/2 and serve hot or warm.