Butter one side of each piece of rye bread. Place 4 pieces of bread butter side down on a plate or cutting board. Spread 1 tablespoon of the Russian dressing on each of the 4 pieces of bread. Cover each piece with ¼ cup of the sauerkraut, 2 oz. of sliced pastrami, and 1 slice of Swiss cheese. Top with the remaining pieces of buttered rye bread, buttered side up.
Heat a cast iron skillet or non-stick pan over medium heat. Place sandwiches in the hot pan and cook on each side until the bread is golden brown and the cheese is melty, about 2-3 minutes per side. Remove from the pan and serve warm.
