Combine the day old mashed potatoes with the egg yolk, flour, cheese, chives, mustard powder, and salt in a medium bowl. Mix well so that all ingredients are combined; then line a baking sheet with parchment paper.
Next, form 1-inch size balls with the mixture and place them on a baking sheet; then refrigerate for at least one hour.
Add approximately 1-2 cups of oil to a Dutch oven or pot (or use a deep fryer. You just need to make sure that the puffs can be submerged in the oil.)Heat the oil to at least 350 degrees F; then add the potato puffs and fry until golden brown; approximately 5 minutes. (Make sure as to not overcrowd the pot so you may have to do this in batches.)
Remove the puffs from the oil using a slotted spoon and drain on a paper towels to remove excess oil. Serve hot.
