In a large bowl, beat the eggs until foamy. Gradually add the sugar, beating constantly. Stir in the milk, shortening and vanilla. Sift together the flour, baking powder and salt. Add to the dry ingredients, mixing well. Cover and chill the dough for 30 minutes to 1 hour for easier handling. Preheat the oven to 450 degrees. Spray a baking sheet with vegetable cooking spray. Roll out or pat the dough on a lightly floured board to a 1/2 inch thickness. Cut with a doughnut cutter. Place the doughnuts and holes on the baking sheet, about 1-inch apart. Bake for 10-15 minutes or until golden brown. Brush each doughnut and doughnut holes with melted butter and roll in cinnamon/sugar to coat all sides. Makes about 36 doughnuts.
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