Start by preheating your stovetop or electric griddle to medium heat.
Place a large skillet or frying pan on the stovetop over medium heat.
Butter one side of each bread slice.
Lay out all the bread slices on a clean surface, buttered side down.
Spread the vegetarian Russian dressing on the non-buttered side of each bread slice.
Layer the vegetarian deli slices on half of the bread slices.
On the remaining bread slices, layer the Swiss cheese followed by the sauerkraut.
Carefully join the two halves together, creating sandwich pairs.
Place the sandwiches on the preheated griddle or skillet and cook for approximately 3-4 minutes per side, or until the bread is toasted and the cheese has melted.
Use a spatula or tongs to flip the sandwiches halfway through cooking.
Once both sides are golden brown and the cheese is melted, remove the sandwiches from the heat.
Optionally, you can wrap the sandwiches in aluminum foil and place them in a preheated oven at 350°F (175°C) for an additional 5 minutes to ensure the cheese is fully melted.
Carefully unwrap the sandwiches and serve them hot.