Combine the chopped corned beef, well-squeezed sauerkraut, torn Swiss cheese and caraway seeds, if using, in a bowl, mixing until evenly distributed.
Lay a wrapper in a diamond shape and spoon 1/3 cup of the filling onto the lower third, pressing it into a neat log so no stray sauerkraut strands poke out past the edges.
Fold the bottom point over the filling, fold in both sides, and roll tightly, sealing the final corner with egg wash.
Repeat with the remaining wrappers, keeping unused ones under a damp paper towel.
Air fry at 380°F: arrange seam side down with space between rolls, spray with oil, and cook 8 minutes. Flip and cook 4 to 5 minutes more, until deep golden and the cheese inside has fully melted (check one by pressing gently; it should feel soft, not firm).
Or bake at 400°F on a parchment-lined sheet, brushed with butter, for 15 to 17 minutes, flipping once.
Whisk the mayonnaise, ketchup, relish and paprika together for the dip.
Let the egg rolls rest 3 minutes; the melted Swiss holds its heat and will burn a careless tongue. Serve with the Thousand Island dip.
Good to Know
No corned beef on hand: pastrami chopped small works just as well and leans a little smokier.