In a medium bowl combine 1/2 cup mayonnaise, 2 tbsp ketchup, 1 tsp prepared horseradish, 1 tsp Worcestershire sauce, 2 tbsp sweet pickle relish, 1/2 tsp paprika, 1/4 tsp salt and 1/4 tsp black pepper. Whisk until smooth and well blended. Taste and adjust seasoning (add a touch more horseradish for heat or more relish for sweetness). Refrigerate while you prepare the rest; the flavors meld in 10–15 minutes.

Sandwich

Prep sauerkraut and bread

If sauerkraut is very wet, place it in a fine-mesh sieve and press lightly to remove excess liquid (you want it moist but not dripping). Butter one side of each of the 8 bread slices with the softened butter (about 1/2 tbsp per slice).

Build sandwiches

Place four slices of bread butter-side-down on a clean work surface. Spread about 2 tbsp of the prepared Russian dressing evenly on each slice. Top each with 4 oz (about 4 oz by weight) of sliced roasted turkey (divide the 16 oz evenly among 4 sandwiches). Distribute 1/4 cup sauerkraut over the turkey on each sandwich, then top with 2 slices of Swiss cheese. Finish with the remaining 4 bread slices, butter-side-up.

Cook until golden and melty

Heat a large skillet or griddle over medium-low to medium heat. Place sandwiches in the skillet (work in batches if necessary). Cook for 3–5 minutes per side, pressing gently with a spatula or using a heavy pan on top to ensure even contact, until bread is deep golden brown and the cheese has melted. If bread is browning too quickly before cheese melts, lower the heat and cover the skillet for 1–2 minutes to trap heat and finish melting.

Slice and serve

Transfer sandwiches to a cutting board and let rest 1 minute, then slice each sandwich diagonally in half. Serve immediately with dill pickle spears and potato chips if desired.