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Cream the butter; add sugar, one spoonful at a time, alternating with a spoonful of beaten eggs.
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Beat into a light cream.
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Sift flour with baking powder, salt and divide into 3 parts.
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Mix milk and vanilla together.
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Add to the creamed ingredients and then add to the dry ingredients.
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Add flour just enough to create a soft dough.
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Cover and chill from 4 to 12 hours.
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The next day, remove 1/3 of dough from the refridgerator; keep the rest cold.
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Roll to 1/3" thick on floured board.
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Cut and let stand for 15 minutes before cooking.
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Fry in 3" of cooking oil- 375 degrees on medium-high.
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Place 3 doughnuts at a time in the pan so the oil doesn't cool down.
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Cook 4 minutes on each side until golden brown.
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Drain on brown paper.
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Sprinkle a mixture of sugar and cinnamon over the warm doughnuts and serve.
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These freeze very well so you can remove a few at a time for eating anytime!