This recipe sheet is virtually identical to the previous entry for raised and cake doughnuts. Each type would be cooked in hot oil. Let the dough cook for a bit, then turn it over so the other side cooks. I recall reading (though not from where exactly) that the oil should be deep enough for the dough to initially sink. It then rises to the top of the oil, at which time it should be turned over.
Raised Doughnuts – Sweet dough
sugar 3/4 cup
salt 1 teaspoon
Shortening 1 stick
eggs 3
flour 3 1/2 cups
Milk 1/2 cup
1 yeast in 1/2 cup warm water
Cake doughnuts
3/4 cup of sugar
shortening 1 teaspoon
1 teaspoon salt
1/2 teaspoon of nutmeg or cinnamon
eggs 3
milk about 1 cup
1 teaspoon vinegar
3 teaspoon baking powder
flour to make a thick dough
Gram's Recipe Box 
Love the original written recipe!
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I actually did a cake doughnut experiment a while back with baking them. They came out very similar to a biscuit in terms of looks and texture of the finished product, but they tasted just like a cake doughnut. Slightly healthier when you still NEED doughnut flavor but don’t want all that oil. Okay, the powdered sugar didn’t stick exactly properly, but they were still quite passable.
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What if you rolled them in granulated sugar before baking? That might be something to try. Do you remember how long and at what temp? Might be fun!
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