Preheat your oven to 400°F (200°C) if baking the Reuben Balls, or heat oil in a frying pan if frying.
In a mixing bowl, combine the chopped corned beef, shredded Swiss cheese, chopped sauerkraut, breadcrumbs, egg, Dijon mustard, garlic powder, salt, and pepper. Mix until evenly combined.
Using your hands, form the mixture into small balls, about 1 inch in diameter. Place them on a baking sheet lined with parchment paper, leaving space between each ball.
If baking, drizzle the balls with olive oil. Bake in the preheated oven for 15-20 minutes or until golden brown. If frying, cook the balls for about 3-4 minutes on each side until they are golden and crisp.
While the Reuben Balls are cooking, prepare the Spicy Thousand Island Dipping Sauce. In a small mixing bowl, whisk together the mayonnaise, ketchup, sweet pickle relish, hot sauce, lemon juice, salt, and pepper until smooth.
Once cooked, remove the Reuben Balls from the oven or frying pan and let them cool slightly before serving.
Serve the Reuben Balls warm with the Spicy Thousand Island Dipping Sauce on the side.