In a large bowl, combine the mashed potatoes, cheddar cheese, Parmesan cheese, green onions, garlic powder, onion powder, salt, and black pepper. Mix until well combined.
Using your hands, form the potato mixture into balls about 1 to 1.5 inches in diameter. Place the balls on a baking sheet lined with parchment paper.
In a shallow dish, beat the eggs. In another shallow dish, place the breadcrumbs.
Dip each potato ball into the beaten eggs, allowing any excess to drip off, then roll in the breadcrumbs until fully coated. Return to the baking sheet.
Heat about 2 inches of vegetable oil in a deep skillet or pot over medium heat until it reaches 350°F.
Carefully add a few potato balls to the hot oil, frying them in batches to avoid overcrowding. Fry for about 3-4 minutes or until golden brown, turning occasionally.
Use a slotted spoon to remove the balls from the oil and place them on a paper towel-lined plate to drain excess oil.
Serve warm with your favorite dipping sauce.