Raised Doughnuts

I'm posting this in answer to a request. I have added a few suggestions, based on my experience with yeast doughs, but the recipe is from Betty Crocker's Cookbook, 1969. I have made these and they turned out well, but it was a very long time ago. The cooking time is my guess for the total recipe, not for each doughnut. Both prep times and cooking times are approximations.

• Ready In: 3 hrs 45 mins
• Yields: 24 doughnuts

Ingredients

• 1⁄4 cup warm water
• 2 1⁄4 teaspoons dry yeast
• 3⁄4 cup  lukewarm milk
• 1⁄4 cup sugar
• 1  teaspoon salt
• 1  egg
• 1⁄4 cup shortening
• 3 3⁄4 cups flour (about, divided)

• Glaze for doughnuts

• 1⁄3 cup boiling water
• 1  cup confectioners' sugar

Directions

1. Place warm water in a large mixing bowl.
2. Sprinkle yeast over the surface of the water; wait a few minutes then stir to dissolve.
3. Mix in milk, sugar, salt, egg, shortening, and 2 cups flour and beat until smooth.
4. Mix in up to 1¾ cups more flour, until you get a dough that can be handled.
5. (Too soft is better than too stiff.) Turn dough onto lightly floured surface; knead until smooth and elastic, about 5 minutes.
6. Place in a greased bowl; turn greased side up and cover with oiled plastic wrap.
7. Let rise in a warm place until double, about 1½ hours; punch dough down.
8. (When the weather is warm, the dough will rise more quickly, do not let it rise past double.) Let rise again until almost double, about 30 minutes; roll dough 3/8 inch thick on lightly floured surface.
9. Cut with a doughnut cutter that has been floured.
10. Let rise, uncovered, on waxpaper until double and very light, 30 to 45 minutes.
11. Heat oil to 375°.
12. Drop doughnuts into hot fat.
13. Turn doughnuts as they rise to the surface.
14. Fry 2 to 3 minutes or until golden on both sides, being careful not to prick them.
15. Carefully remove from fat and drain.
16. Roll in sugar or glaze while warm.
17. To glaze, blend ingredients for glaze and dip warm doughnuts into it.