Prepare the mashed potatoes by boiling peeled and chopped potatoes until tender, then mash and cool completely.
In a large mixing bowl, combine cooled mashed potatoes with cheddar cheese, Parmesan cheese, flour, eggs, garlic powder, onion powder, salt, and black pepper. Mix until well combined.
Form the mixture into balls about 1 to 1.5 inches in diameter and place them on a baking sheet lined with parchment paper.
Coat each ball in breadcrumbs and heat oil in a deep skillet or pot to 350°F. Fry the puffs in small batches for 3-4 minutes until golden brown.
Remove the puffs with a slotted spoon and let them drain on paper towels. Serve warm.