If you’re using freshly made mashed potatoes, let them cool to room temperature or refrigerate briefly so they’re easier to handle. Leftover mashed potatoes work beautifully here.
In a bowl, combine the mashed potatoes, shredded cheddar cheese, egg, salt, pepper, garlic powder, and chopped chives or parsley. Mix until evenly incorporated — don’t overwork, just make sure the cheese is distributed.
Prepare a dredging station: place the flour in one shallow dish, beat an extra egg (or two tablespoons of milk mixed with one beaten egg) in a second dish, and place the breadcrumbs in a third dish. These three steps create a sturdy coating.
Scoop about 2 tablespoons of the potato mixture and roll it into a compact ball using lightly floured hands. If you prefer larger croquettes, use more mixture; adjust cooking time slightly.
Roll each ball first in flour, then dip into the beaten egg, and finally coat thoroughly with breadcrumbs. Press the breadcrumbs gently so they adhere evenly.
Heat 1/2 inch of vegetable oil in a heavy skillet over medium heat, or heat oil in a deep pot to 350°F (175°C) for deep frying. Test readiness by flicking a few breadcrumbs into the oil—they should sizzle immediately.
Fry the potato balls in batches, avoiding overcrowding. If shallow frying, turn them gently to brown on all sides; if deep frying, gently lower them in and fry until golden, about 3–4 minutes total. Adjust time based on size.
Transfer cooked balls to a paper towel-lined plate to drain excess oil. Season lightly with a pinch of salt while hot if desired.
Let them rest for a minute, then serve warm with your choice of dipping sauce. Enjoy immediately for the best contrast of crisp exterior and soft, cheesy interior.