Butter one side of each slice of rye bread. Place 4 slices butter-side down on your work surface.
Spread about 1 tablespoon of Russian dressing on each unbuttered side. Layer each with 1 slice of Swiss cheese.
Divide corned beef evenly among the 4 sandwiches, piling it on top of the cheese. Add 1/4 cup sauerkraut to each sandwich.
Top each with another slice of Swiss cheese and drizzle with a little more Russian dressing. Place remaining bread slices on top, butter-side up.
Heat a large skillet or griddle over medium heat. Cook sandwiches for 3-4 minutes per side, pressing down gently with a spatula, until golden brown and cheese is melted.
Cut sandwiches in half diagonally and serve immediately with extra Russian dressing on the side for dipping.