1. Prepare mashed potatoes peel and cut up potatoes. Cover with water. Boil until done. Save the potato water to mix with yeast. Mash the potatoes with a little bit of milk. DO NOT ADD SALT OR PEPPER.
2. Scald 1 quart milk. Add 1 cup. (2 sticks) cut up margarine, stir to melt margarine. Set aside to cool.
3. Dissolve 2 pkgs. dry yeast in 1 cup warm (105-110F) potato water.
4. Mix together 1 cup sugar, 1 cup mashed potatoes, 1 tsp. baking soda, 1 tsp. baking powder, and 1 tsp. vanilla in LARGE pan or container. Stir in the cooled milk mixture (item No. 2) and the yeast mixture (Item No. 3). Mix vigorously. Set mixture in a warm place and do not cover. (I used to put mine over small pilot light on a gas stove using a metal pan).
5. Let the mixture set for about 30 minutes until it "rises" and gets foamy and "bumpy" looking.
6. Whisk lightly 4 eggs in a bowl. Add to yeast batter. Stir in 1 Tbsp. salt. Add approximately 12 cups of flour, 3 cups at a time, stirring vigorously after each 3-cup addition using a large mixing spoon with holes in it. The batter will get very stiff. Set pan back in a warm place and put a tea towel over it. Let it rise until double in bulk, about 1 hour.
7. Mix together 1 box of powdered sugar and a small glass (empty pimiento cheese spread glass) of milk. Mix well and let set. It will dissolve better if mixed well ahead of glazing time. You may eventually need more than this, but you will see what you will need in time to mix more.
After dough has risen to double in bulk, work with it on a well-floured surface (or pastry cloth). Sprinkle about 1 to 1-1/2 cup flour onto surface and spread it approximately 1/2 to 1-inch deep.
Spoon out a workable amount, but not all, of the "sticky" dough into the flour pile. Don't knead the dough. Just "poke or pat" it with your fingers in the flour until with very little handling you can roll it out gently to a thickness of about 3/4-inch.
Use a large doughnut cutter with sharp edge to cut out doughnuts. Place the doughnuts on well-greased cookie sheets or plastic trays (smooth serving trays work good). Place the sheets/trays with doughnuts in a warm place, covering with tea towels while they are rising.
Heat shortening (Crisco is very good) to 375F. Start frying the doughnuts that were cut first and have had the longest time to rise. Fry a few at a time until golden brown. Do not put too many in at one time or it will lower the temperature of the shortening. The 375F must be maintained as closely as possible to prevent the doughnuts from absorbing the grease.
Remove the fried doughnuts and drain them on several layers of paper toweling. When they are drained, dip them into the glaze on both sides of the doughnut, and "string" 4 or 5 doughnuts, not touching each other, onto a wooden spoon handle and lay the spoon across the glaze bowl to allow the excess glaze to drop back into the bowl for a minute or two. Then push the doughnuts off onto wax paper, standing them on end as much as possible in rows.
When the doughnuts are thoroughly cooled, package them in plastic bags for freezing (that is if there are any left after eating them as you goha!). When you want some that have been frozen, preheat your oven to 350F, and put doughnuts on a cookie sheet and heat for about 3-5 minutes. They will be even more tender than they were when first fried. You can also microwave them on 50% power until they are tender, approximately 30 seconds per doughnut. Of course they are WONDERFUL fresh!