In a large bowl, combine the corned beef, sauerkraut, Swiss cheese, breadcrumbs, cream cheese, Dijon mustard, garlic powder, onion powder, salt, and pepper. Mix until well combined.

Form the mixture into small balls, about 1 inch in diameter. Dip each ball into the beaten egg, then roll in additional breadcrumbs if desired for extra crunch.

Heat oil in a deep skillet or fryer over medium heat. Once hot, carefully add the Reuben balls in batches, frying until golden brown on all sides, about 3-4 minutes. Remove and drain on paper towels.

For the dipping sauce, whisk together the mayonnaise, ketchup, relish, hot sauce, salt, and pepper in a small bowl until smooth.

Serve the Reuben balls warm with the spicy Thousand Island dipping sauce on the side.