In a large mixing bowl, combine the mashed potatoes, chopped green onions, shredded cabbage, shredded cheddar cheese, milk, egg, salt, and black pepper. Mix until well combined.
Using your hands, form the mixture into small balls, about 1 to 1.5 inches in diameter. Place the balls on a baking sheet lined with parchment paper.
Roll each ball in breadcrumbs until fully coated. Return them to the baking sheet.
In a large skillet, heat about 1 inch of vegetable oil over medium heat. Once the oil is hot, carefully add the potato balls in batches, ensuring not to overcrowd the pan.
Fry the potato balls for about 3-4 minutes on each side, or until they are golden brown and crispy. Use a slotted spoon to transfer them to a paper towel-lined plate to drain excess oil.
Serve warm, garnished with additional green onions if desired.