Instructions:
Preheat a skillet or griddle over medium heat.
Butter one side of each slice of rye bread. These will be the outer sides that crisp up in the pan.
Assemble the sandwiches:
Place two slices of bread butter-side down.
Spread 1 tablespoon of Russian dressing on each slice.
Add 1 slice of Swiss cheese to each.
Pile on 4 ounces of corned beef per sandwich.
Top with about ½ cup of sauerkraut.
Add another slice of Swiss cheese on top.
Spread another tablespoon of dressing on the top slice of bread (non-buttered side), then close the sandwich with the remaining bread, buttered side up.
Grill the sandwiches in the skillet for about 4–5 minutes per side, pressing gently with a spatula or sandwich press. Cook until the bread is golden brown and crispy, and the cheese is fully melted.
Remove and let rest for a minute before slicing each sandwich in half.