In a medium mixing bowl, beat eggs, sugar, and butter. Add pumpkin puree, mix in well. For the dry ingredients, combine the flour, baking powder, baking soda, salt, and pumpkin spice. Begin to marry the pumpkin batter and alternate with the evaporated milk, folding in gently. Refrigerate the batter to firm for approx 1 hour before kneading. Turn onto a lightly floured work-surface and knead well. Roll to approximately ¾'' in thickness. Cut with a 2½'' doughnut cutter. (Alternatively, cut with the small rim of any glass jar or cup and use a small bottle to cut out the hole.) Fry doughnuts and doughnut holes, a few at a time, until golden (approximately 1-2 minutes on each side). Remove using a slotted spoon or a spider and allow the excess oil to drain on paper towels. For the icing, whisk together all ingredients in a medium mixing bowl. Spread over cooled doughnuts with a teaspoon (place on a wire rack over a sheet tray, if desired).
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