This was the best by far to me. I didn't post it here because of the need to use approved oil. There are many many brands so I'll just let you know that I use wesson oil (not shortening). Please check the Feingold food list for different options. If you know that this diet has helped you it would really benefit your family to have a food list at least for a year.
The key to these is to keep the dough very very very soft. I make it the night before and stick it in the fridge overnight. Then in the morning, I flour the cutting board, roll out gently, and cut with my doughnut cutter. By morning it only needs a little flour to roll but the dough can still be nice and light. They turn out MUCH different if you put too much flour in.
We do a light glaze with powdered sugar and water and dip the whole doughnut in.