Mary Burrill's Baked Doughnuts

Boil a scant cup of potato in plain water, mash smoothly as possible and reserve 1/4 cup water.
Scald 1 cup of milk, and melt 3/4 cup shortening, 1/2 cup sugar and 1 teaspoon salt
Dissolve one Tablespoon of yeast in the warm potato water.  Allow to proof.
Combine all ingredients and add two beaten eggs.
(I add 1/2 t mace, nutmeg or cinnamon and 1 t vanilla, but the old recipe does not call for it.)
Add a cup of flour and beat till smooth.
Add more flour until you approach 3 1/2 additional cups maximum, beating it in and later kneading it in.  Use as little flour as possible to be able to handle the dough.
Knead the dough well...10 to 20 minutes.
Place in a covered bowl and allow to rise till at least double.

Roll to 1 inch thick and cut in rounds or doughnuts.
Place on buttered baking sheets not touching.
Allow to rise till double again.
Bake at 425 F till delicately brown...less than 12 minutes, but keep checking.  You know raised doughnut color!
Brush the doughnuts with melted butter and roll in sugar(I mix mace, nutmeg or other spice into the sugar.)

My sister has had this recipe for almost 50 years and this is the first time we tried it, just before I left for overseas.  They are ABSOLUTELY DIVINE!!!
Makes 2 dozen depending on your cutter, and they last well, covered for three days.  Try filling them with sweetened Moscarpone(or mixed with cocoa or liquor), jelly, pudding, lemon curd or cannoli filling.  You could also split them and fill them with VERY SOFT cream cheese mixed with maraschino cherries, whole berries, sweet ham/prosciutto or jams to make sweet sandwiches for a party or shower.  Vary the spices or omit depending on what you are filling them with.
Sorry I do not have a picture.  They are difficult to upload here and also...they were eaten too fast...light as air and a lovely taste.