Place a 10-inch skillet over medium heat. Melt together cream cheese and Russian dressing until combined.
Mix drained sauerkraut and corned beef into the cream cheese mixture. Give it a taste and season with salt & pepper as needed.
Top with shredded Swiss cheese and place under broiler until the cheese is melted. Remember to keep an eye on the dip, it should only take about a minute for the cheese to melt!
Carefully remove from oven and garnish with more shredded corned beef and chopped parsley. Serve warm with rye bread and baguette pieces.