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In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
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In a large bowl, whisk the egg yolks, yogurt, sugar, butter, and vanilla.
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Add the flour mixture to the egg mixture and mix together using a rubber spatula until a smooth dough forms.
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Place dough onto a well-floured surface and dust the top with flour. Roll dough out to about ½ inch thickness.
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Brush off excess flour and cut into shapes using the large Mickey shaped cutter. Add holes in the center of the face and ears using the small round cutter.
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Fill a large pot or dutch oven with about 1 ½ inches of oil. Heat over medium-high until the oil reaches 350 F.
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Fry 1-2 donuts at a time, flipping halfway through until they are puffy and golden, about 4 minutes total. If you want to make donut holes, fry the small cut outs for less time.
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Using a heat-safe slotted spoon or spider, transfer to a paper towel lined wire rack and let cool for 10 minutes.