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1
Stir sugar and yeast into warm milk; set aside until it bubbles, 15 minutes.
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2
Melt butter in microwave oven; set aside to cool to room temperature. Beat together powdered sugar, whole eggs and yolks in small bowl until well-combined.
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3
Beat in rum. Set aside.
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4
Place flour, salt, yeast mixture and egg mixture in bowl of electric mixer with paddle attachment. Beat until flour is combined and dough is stretchy, about 3 minutes. (Or beat by hand 10 minutes.) Add melted butter; mix until well-combined, about 1 minute. Cover bowl with towel; let stand in warm place until doubled in size, about 1 1/2 hours.
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5
Place dough on lightly floured surface. Stretch and pat until 1/4 inch thick.
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6
Cut into 3 inch circles using glass or biscuit cutter. Place1/2 teaspoon of the filling in center of each circle. Fold dough over filling; pinch edges together, making a ball. Place on floured parchment or wax paper. Cover with towel. Let stand in warm place 45 minutes.
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7
Heat shortening in deep-fat fryer, deep saucepan or wok until deep- frying thermometer reaches 360 to 370 degrees F. Have hot fat at least 3 inches deep.
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8
Fry paczkis, a few at a time, until brown on all sides, about 4 minutes. Drain on paper towel-lined plate. Sprinkle with powdered sugar while still warm.