Start heating several inches of oil in a heavy pot.

In a bowl, combine the flour, baking powder, and salt.

Add in the mashed potatoes and stir until smooth.

Lightly beat the egg and stir that in until combined.

When the oil has reached 385 °F (the surface should be shimmering but not yet smoking), carefully drop in blobs of the potato mixture, about a tablespoon's worth each. They should start to bubble and darken instantly; if not, your oil is not hot enough. Don't crowd the pot, because you want to be able to move the puffs around so they get cooked on all sides.

Fry them in batches until they are a dark golden brown, frequently shuffling them around with a wooden spoon. As each batch is done, pull them out with a slotted spoon or deep fryer scoop, let them drain for a few seconds, and move them to a platter with paper towels to absorb the extra oil. They can be kept warm in the oven for a short time, but they are best when they are fresh.