Heat the oven to 350 degrees. Line a baking sheet with parchment paper.
On a lightly floured surface, roll out a pie crust into a 12-inch round. Use a cookie cutter or a saucer and sharp knife to cut 2 6-inch rounds. Transfer them to the baking sheet. Reroll the dough and cut 2 more circles. Repeat with the other pie crust.
Scatter 3 tbsp. sauerkraut on half of each dough round, leaving a 1/2-inch border. Top with 2 tsp. dressing. Layer on 2 beef slices and 2 tbsp. cheese. Moisten the edges of each round, then fold them over the filling to form half-moons. Line up the edges, press them together, and crimp with a fork.
Brush each pie with egg wash and poke 2 slits in the top with a paring knife. Bake until golden brown, about 35 minutes. Let cool for 15 minutes before serving.