In a large bowl, combine the mashed potatoes, cheddar cheese, flour, Parmesan cheese, egg, baking powder, garlic powder, onion powder, salt, and black pepper. Mix until a dough forms.
Lightly flour a clean surface and turn the dough out onto it. Knead the dough gently for about 1 minute until it is smooth.
Roll the dough out to about 1/2 inch thick. Use a donut cutter or two round cookie cutters (one larger and one smaller) to cut out donut shapes.
In a deep skillet or pot, heat about 2 inches of vegetable oil over medium heat until it reaches 350°F.
Carefully place the donuts in the hot oil, a few at a time, and fry for about 3-4 minutes on each side until golden brown. Use a slotted spoon to remove them and drain on paper towels.
Allow the donuts to cool slightly before serving. Enjoy them warm!