Preheat oven to 350°. In a medium bowl, stir together cream cheese and Russian dressing until combined, then fold in 1 cup of Swiss, almost all the corned beef, and sauerkraut and season with pepper.
Transfer dip to a small baking dish and top with remaining ¼ cup Swiss and corned beef. Bake until golden and bubbly, 18 to 20 minutes.
Garnish with parsley and serve with bagel chips.
