In a large bowl, combine the leftover mashed potatoes, cheddar cheese, Parmesan cheese, green onions, and the egg. Mix until well combined. Season with salt and pepper to taste.
Using your hands, form the mixture into small balls or patties, about 2 inches in diameter.
Place the flour in a shallow dish. In another shallow dish, place the breadcrumbs.
Roll each potato ball first in the flour, then dip it in the breadcrumbs, ensuring they are fully coated.
Heat about 1 inch of vegetable oil in a large skillet over medium heat.
Once the oil is hot, carefully add the croquettes in batches, frying them for about 3-4 minutes on each side or until golden brown and crispy.
Remove the croquettes from the oil and place them on a paper towel-lined plate to drain excess oil.
Serve warm with your favorite dipping sauce.