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Meanwhile, place the potatoes in a large pot, cover with water, and bring to a boil, cooking until tender. Drain and pass through a food mill or ricer and place in a large bowl. Add the eggs, flour, sugar, 1/4 cup oil, amaro, juice, and zest of orange and mix well to combine. Add the yeast mixture and knead well, adding more flour if necessary to keep the batter from becoming too sticky. Let the dough rise in a warm place for 1 hour.
Divide the dough into four equal pieces and roll each one out to form a 1 1/2-inch thick dowel. Cut the dowels into 5-inch lengths and form little doughnuts. Place the doughnuts on a well-oiled baking sheet and let rise until they double in volume.
In a tall-sided pot, heat the quart of olive oil to 375 degrees F.
Working in batches, fry the doughnuts in the hot oil until golden brown, about 5 minutes. Remove with a slotted spoon and allow to drain on a plate lined with paper towels. Dust with confectioners' sugar and serve.