1. In a skillet over medium heat, cook ground beef with garlic powder, onion powder, salt, and pepper until browned. Set aside and let cool.
2. In a large bowl, mix mashed potatoes, cheddar cheese, Parmesan cheese, and egg until combined.
3. Divide the potato mixture into equal portions. Flatten each portion in your hand, place a spoonful of ground beef and a piece of shredded cheddar cheese in the center, and seal it into a patty.
4. Coat each patty in flour, dip in beaten egg, and roll in breadcrumbs.
5. Heat vegetable oil in a skillet over medium heat. Fry the patties for 3-4 minutes on each side until golden brown and crispy.
6. Garnish with fresh chives and serve hot.