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In a large bowl, whisk together the water, sugar, and yeast. Set aside for 10 minutes, until bubbly.
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In a small bowl, mix together the egg, salt, and evaporated milk.
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Add the milk mixture to the yeast mixture and stir to combine.
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Add 2 cups of flour and mix to combine, using an electric mixer if needed. Once combined, mix in the shortening.
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Add additional flour, ¼ cup at a time, until the dough begins to pull away from the sides of the bowl and forms a soft dough that is slightly sticky. Form the dough into a large ball and place in a large, greased bowl. Cover with plastic wrap and place in a dark, warm area. Let rise for two hours, until doubled in size.
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Once dough has risen, heat the oil in a heavy pot or dutch oven to 350 F. Roll the dough out on a lightly floured surface to about ½ inch thick. Cut out beignets using a small Mickey Mouse cookie cutter.
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Once the oil is heated, carefully place 3-4 beignets into the oil (depending on your pot size) and let cook for 30-60 seconds per side or until each side is a deep golden brown (depending on how much your oil cools while being used it could take 1-2 minutes per side).
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Remove cooked beignets and drain on paper towels. Let cool for 3-5 minutes and cover with powdered sugar. Serve while hot.