Start by peeling and chopping your potatoes into even chunks. Place them in a large pot of salted water and bring to a boil over medium-high heat. Cook for about 15-20 minutes, or until the potatoes are tender and easily pierced with a fork. Once done, drain the water and mash the potatoes until smooth. Allow the mashed potatoes to cool slightly before mixing with other ingredients.

In a large mixing bowl, combine the cooled mashed potatoes, half of your shredded cheese, chopped green onions, salt, pepper, and the large egg. Using a spatula or wooden spoon, mix until all ingredients are well incorporated and you achieve a thick, creamy consistency.

Scoop about a tablespoon of the potato mixture and roll it into a small ball or puff shape using your hands. Place the formed bites on a parchment-lined baking sheet to prepare for coating.

Pour breadcrumbs into a shallow dish, adding some extra seasoning if desired. Taking each potato puff from the baking sheet, roll it in the breadcrumbs, ensuring it is fully coated.

Heat a generous amount of oil in a deep skillet over medium-high heat. Carefully add the coated potato puffs to the hot oil in small batches. Fry each side for about 3-4 minutes, or until they turn golden brown and crispy. Alternatively, for a healthier option, bake the puffs at 400°F (200°C) for about 20 minutes until they're golden and crunchy.

Once cooked, transfer the Cheesy Mashed Potato Puff Bites to a plate lined with paper towels to drain excess oil. Serve them warm with your favorite dipping sauce.