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1
Bring the potato and water to cover to a boil in a small saucepan. Reduce the heat and simmer until the potato is tender, about 15 minutes. Drain the potato, then mash until smooth. Let cool completely, at least 30 minutes.
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2
Transfer 1/2 cup mashed potato to a medium bowl (discard the remaining potato) and beat in the egg, milk, 1/2 cup of the sugar, and vanilla until combined. Whisk the flour, baking powder, salt, cinnamon, and nutmeg together in a large bowl. Make a well in the center of the flour mixture and add the potato mixture. Stir to form a moist and sticky dough.
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3
On a heavily floured work surface, roll the dough into an 18 by 14-inch rectangle about 1/4-inch thick. Cut the dough into 1 1/2-inch wide strips, make a slit in each strip, and twist the legs around each other twice to shape the dough to resemble crossed legs. Transfer the crullers to a floured baking sheet and refrigerate until ready to fry. (The crullers may be covered with plastic wrap and refrigerated for up to 24 hours.)
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4
Heat the oil in a large Dutch oven over medium heat until the temperature reaches 350 degrees. Carefully lower 6 crullers into the hot oil and fry, maintaining a temperature between 325 and 350 degrees, until crisp and deep brown on both sides, about 6 minutes. Using a slotted spoon, transfer the crullers to a plate lined with paper towels and drain for 3 minutes. Toss the crullers in a bowl with the remaining sugar and transfer to a serving plate. Repeat with the remaining crullers, regulating the oil temperature as necessary. Serve.
