Special equipment: a deep-frying thermometer
Whisk together the flour, confectioners' sugar, baking powder, cinnamon, allspice, salt and nutmeg in a large bowl. Pour in the cider and vanilla extract, and whisk to make a smooth batter.
Preheat the oven to 200 degrees F.
Pour enough oil into a heavy-bottomed soup pot so it comes about a third of the way up the sides. Heat the oil over medium heat until a deep-frying thermometer inserted in the oil registers 360 degrees F.
Peel, core and slice the apples into rounds, about 1/3-inch thick. Put some flour in a shallow bowl. Working in batches, dust the apple slices in the flour, then dip in the batter to evenly coat. Carefully add to the oil. Fry, turning once, until golden and crisp, about 5 minutes. Transfer to a rack set on a baking sheet, and keep warm in the oven. Repeat the process until all of the apples are cooked, allowing the oil to return to 360 degrees F between batches.
Dust with confectioners' sugar or cinnamon sugar and serve immediately.
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