Spread 1 tablespoon of the Thousand Island Dressing on each slice of bread. Divide the cheese, sauerkraut, and pastrami among 4 of the slices, and top each sandwich with the remaining bread. Spread the tops of the sandwiches with half of the butter.

Heat a 12-inch (or larger) skillet over medium heat. Add the sandwiches, buttered side down, in batches if necessary, and weight them down with a cast-iron press or another heavy skillet. Cook the sandwiches until golden brown and crisped, 2 to 3 minutes. Butter the top of the sandwiches with the remaining butter, turn them over, and cook them for another 2 to 3 minutes. Transfer the sandwiches to a cutting board, slice them in half, and serve immediately.