Roll out the Basic Sweet Dough as thin as possible. Cut for doughnuts (I never did have a cutter, so I used a glass and a VERY CLEAN thimble to cut the holes).
Let rise till double, then fry in medium hot oil (probably 400° in electric fryer or skillet). Don't try to fry more than 3 or 4 at a time or it will cool your oil. When both sides have been browned, carefully remove and drain well. A paper bag with paper towels over it works well. When dry dip in a thin glaze and place on plates to drain.
The best way to make doughnuts is just to stand there and fry while everyone else eats -- that way you don't have to worry where to put them. This makes a big batch.