Boil potatoes in salted water for 15-20 minutes until fork-tender, drain, and mash until smooth. Mix in half of shredded cheese, salt, and pepper.

Combine mashed potatoes, remaining cheese, green onions, and egg in a large mixing bowl. Stir well until evenly blended.

Scoop the mixture into small balls or puffs, about one inch in diameter. Place on a parchment-lined baking sheet.

Roll each potato puff in breadcrumbs until fully coated. Set back on the baking sheet.

Heat about 1 inch of oil in a deep pan over medium-high heat. Fry puffs for about 3-4 minutes until golden brown or bake at 400°F (200°C) for 20 minutes, turning halfway.

Transfer cooked puffs to a paper towel-lined plate to absorb excess oil. Serve warm with dipping sauces.