Butter one side of each of the slices of rye bread. Spread Russian dressing on the unbuttered sides. Layer the sandwich in the following order: 1 slice of Swiss cheese, corned beef, sauerkraut, and the remaining slice of cheese. Top with the second slice of bread, dressing-side down.
Heat a nonstick skillet over medium heat. Grill the sandwich until the bread is golden and crispy and the cheese is melted, about 3 minutes per side. Gently press down on the sandwich occasionally with a spatula as it cooks. Serve immediately with pickles and potato chips, French fries, or vinaigrette potato salad.