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1
Pour warm milk into the bowl of a stand mixer. Sprinkle yeast on top and stir until dissolved. Let stand until foam rises, about 5 minutes.
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2
Add the sugar, salt, vanilla and eggs to the bowl. Whisk until combined well. Use your mixer's dough hook and add flour. Combine well, occasionally scraping down bowl.
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3
Add the butter, in pieces, and mix until smooth. The dough batter will be sticky.
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4
Place dough in a well-oiled (sprayed with Pam) bowl. Refrigerate and let rise for 3-4 hours or until doubled in size.
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5
Line with parchment and lightly flour 2 large baking sheets..
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6
Dust some flour on a clean surface and roll out dough to 1/2 inch thickness. Using a 1/2-inch cookie cutter, cut into discs. Lay the discs on the lined, floured baking sheets.
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7
Dust discs with more flour, cover with plastic wrap and let rest in a warm place for 30 minutes up to 1 hour.
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8
On medium high flame, heat oil in a large deep pot. Deep fry thermometer should register between 365- 370u00b0 F. Lower the doughnuts using a large slotted spoon into the oil. Fry in batches, a few at a time, until golden brown, about 1 1/2 minutes, remembering to gently push, roll around and submerge doughnuts in oil. Take out and drain on paper towels.
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9
Fit a pastry bag with round tip #3. Fill bag with jam or desired filling. Insert the tip into a side of the doughnut. Apply light pressure and fill. Set aside.
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10
Dust with confectioner's sugar.
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11
Serve warm.
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12
Loosely adapted from Food Network Magazine's Jelly Doughnuts.