Spread 2 tablespoons Russian dressing on one side of each of 4 slices of bread. Place 1 cheese slice on each bread slice. Divide sauerkraut and corned beef among sandwiches. Spread mustard on remaining 4 slices of bread, and place on top of sandwiches, mustard side down.
Spread half of butter evenly on tops of sandwiches; place sandwiches on a hot griddle or skillet, buttered side down. Cook until bread is golden. Spread remaining butter evenly on ungrilled sides of sandwiches; turn carefully, and cook until bread is golden and cheese is slightly melted. Serve immediately.