In your mixing bowl, mix 1 envelope of yeast with 1/4 cup lukewarm water. Stir until frothy. Heat 1 cup rice milk and add to yeast. Add 1 1/2 cups flour and beat until smooth. Cover and let double in size. This may take several hours. I often sit it near the oven or a *warm* place.
Cream shortening, salt, sugar and egg. Add egg mixture to the yeast mixture. Add 2 more cups flour. Knead the flour into the mixture until smooth and dough is not sticking to your hands. You may need a little more flour. Let rise until double again.
Roll out dough 1/2 inch thick and cut out doughnuts. Let the doughnuts rise 1-2 hours. Then deep fry in oil. I also fry the doughnut holes. Fry until golden brown.
Dip in sugar or dairy free icing when warm or let cool and sprinkle with powdered sugar.
Egg may be substituted with egg replacer.