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Dissolve yeast in 1/4 c warm water in a small bowl.
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Add milk, 1/2 c sugar, salt, eggs, shortening and 2 c. of the flour. Beat on low-speed, scraping the bowl constantly for about 30 seconds.
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Beat on medium speed, scraping the bowl occasionally for 2 minutes. Stir in remaining flour until smooth.
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Cover and let the dough rise in a warm place until it doubles, approximately 50 - 60 minutes.The dough is ready when indentation remains when touched. (You can mix this all together in a stand mixer if you prefer)
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Turn the dough onto a generously floured surface; roll around lightly to coat with flour. Gently roll the dough 1/2 inch thick with a well-floured rolling pin. Cut with a floured doughnut cutter. Cover and let the doughnuts rise again until double, 30-40 minutes.
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Heat oil (2-3 inches) in a deep fryer or Dutch Oven to 350 degrees. Slide the doughnuts into the hot oil with a wide spatula. Turn the doughnuts as they rise to surface.
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Fry until golden brown, about 1 minute on each side. Remove them carefully from the oil (do not prick surfaces) and drain. Serve sugared or spread with cream or chocolate glaze while they are still warm.