In a large bowl, combine the mashed potatoes, glutinous rice flour, Parmesan cheese, garlic powder, onion powder, salt, and black pepper. Mix until well combined and a dough forms. If using, fold in the chopped green onions.
Divide the dough into small balls, about 1 inch in diameter. Flatten each ball slightly to form a patty.
Heat the vegetable oil in a large skillet over medium heat. Once hot, carefully add the potato patties to the skillet, making sure not to overcrowd the pan.
Fry the patties for about 3-4 minutes on each side, or until golden brown and crispy. Remove from the skillet and drain on paper towels.
Serve warm as a snack or appetizer with your favorite dipping sauce.