In a mixing bowl, combine the mashed potato, granulated sugar, egg, melted butter, and milk, stirring until the mixture is smooth.
In a separate bowl, sift together the all-purpose flour, baking powder, and salt, then gently fold this dry mixture into the wet ingredients until just combined.
Heat vegetable oil in a deep pot over medium heat until it reaches 350°F (175°C).
Using a spoon or a small scoop, drop spoonfuls of the batter into the hot oil, shaping them into doughnut circles.
Fry the doughnuts for 2 to 3 minutes on each side, or until they are golden brown and cooked through.
Once cooked, remove the doughnuts with a slotted spoon and let them drain on paper towels.
While they are still warm, dust the doughnuts with powdered sugar before serving.
