For the egg rolls: Place 1 egg roll wrapper on a dry work surface with the points of the wrapper facing up and down (like a diamond). Place about 1 ounce of corned beef in the middle of the wrapper. Add about 2 tablespoons of Swiss cheese, a scant 2 tablespoons of sauerkraut, and a pinch of caraway seeds, if using. Brush the edges of the wrapper with the egg. Fold the left then right points of the wrapper in toward the center. Fold the bottom point over the center. Roll toward the remaining point to form a tight cylinder. Press the edges to seal. Place on a plate and cover with a dry towel. Repeat the process with remaining wrappers, corned beef, sauerkraut, Swiss cheese, and caraway seeds.

For the Russian dressing: In a medium bowl, whisk together the mayonnaise, chili sauce, horseradish, vinegar, onion powder, paprika, and Worcestershire sauce until well-combined. Cover and refrigerate until ready to use, up to 1 week.

For shallow frying: Preheat the oven to 250°F. In a large cast-iron skillet, heat ½ inch of oil over medium heat until it registers 350°F. Fry 4 egg rolls, turning occasionally, until golden brown on all sides, 1 to 2 minutes. Transfer to a wire rack set in a baking sheet and keep warm in the oven. Continue frying until all the egg rolls are cooked.

For the air fryer: Preheat the air fryer to 400°F, if required. Spray the air fryer basket with cooking spray. Brush the tops of the egg rolls with vegetable oil. Working in 3 batches (4 at a time), place the egg rolls in the basket and cook for 7 minutes. Flip the egg rolls over and brush with more oil. Cook for 5 minutes more. Brush with more oil before serving, if you like.

Serve hot with the Russian dressing.