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1
Place 1/3 cup of the warm milk in the bowl of an electric mixer. Stir in the yeast and set aside for five minutes or so. Be sure your milk isn't too hot or it will kill the yeast. Stir the butter and sugar into the remaining cup of warm milk and add it to the yeast mixture. Stir in the eggs, flour, and salt - just until the flour is incorporated. With the dough hook attachment of your mixer beat the dough for a few minutes at medium speed. If your dough is overly sticky, add flour a few tablespoons at a time. If it is too dry, add more milk a bit at a time. The dough should pull away from the sides of the mixing bowl and eventually become supple and smooth. Turn out dough onto a floured surface, knead a few times, and shape into a ball.
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2
Transfer the dough to a buttered (or oiled) bowl, cover, put in a warm place, and let rise for an hour or until the dough has roughly doubled in size.
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3
Punch down the dough and roll it out 1/2-inch thick on your floured countertop. Use a 2-3 inch cookie cutter to stamp out circles. Transfer the circles to a parchment-lined baking sheet. Cover with a clean cloth and let rise for another 45 minutes.
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4
Bake in a 350 degree oven until the bottoms are just golden, 8 to 10 minutes - start checking around 8 minutes. Transfer doughnut to cooling rack to cool completely.
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5
To fill doughnuts: Mix pudding ingredients. Put prepared pudding into a pastry bag fitted with a long tip, poke the tip into the doughnut and fill each doughnut with about 2 tablespoons of pudding.
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6
To make icing: mix the powdered sugar, vanilla, milk, and margarine together to make a VERY thin icing. Frost the top of the doughnuts and then dip the tops into a bowl of coconut flakes. I toasted some of the coconut flakes before hand because I love toasted coconut.
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7
Eat immediately and freeze any leftovers in an air-tight container. To thaw, microwave on medium power for about 30 seconds or until thawed.
