Place the sauerkraut in a fine mesh strainer and press or squeeze to remove excess liquid; then transfer to a small bowl. Toast all 8 slices of rye bread lightly (about 1–2 minutes) until just golden — this helps prevent sogginess.

Butter bread

Spread softened butter evenly on one side of each toasted rye slice. The buttered side will be the outside of the sandwich for grilling.

Assemble sandwiches

On the unbuttered side of 4 bread slices, spread about 1 tablespoon of thousand island dressing each. Top each with 2 slices Swiss cheese, then divide the pastrami evenly (approximately 75 g per sandwich) and then the turkey (about 50 g per sandwich). Scatter about 1/4 cup drained sauerkraut over the meat, then season lightly with freshly ground black pepper. Place the remaining Swiss cheese slice on top of the sauerkraut (this helps bind). Close each sandwich with a buttered slice of rye, butter side out.

Grill sandwiches

Heat a large skillet or griddle over medium heat. Place two sandwiches in the skillet (buttered side down). Cook 3–4 minutes until the bread is golden and a crust forms. Press gently with a spatula or a weighted pan. Flip carefully and cook the second side 3–4 minutes until golden and the cheese is fully melted (if cheese is slow to melt, cover the pan for 1–2 minutes to trap steam). Repeat with remaining sandwiches.

Rest and slice

Transfer grilled sandwiches to a cutting board and let rest 1 minute. Slice each sandwich diagonally (or in half) and serve immediately.

Optional (for serving)

Serve sandwiches with dill pickle quarters and potato chips on the side.