Add sugar and yeast to warm water and set aside for 5 minutes. Mixture will become foamy.
Beat together egg and milk. Add 1/2 the gluten-free flou8r and the salt and mix together.
Add the shortening and mix into the flour mixture.
Add in half the yeast mixture and half the remaining flour. Stir and then add the remaining flour and yeast. The dough should begin to pull away from the sides of the bowl. Add more flour if dough is still sticky.
Cover the dough with waxed paper or a towel and let the dough rise for 1-2 hours in a warm area. (You can eliminate this rise time if you are in a hurry.)
Place the dough on a floured board or clean countertop that has been dusted with gluten-free flour. Roll the dough until it is about 1/2 inch thick.
Cut squares that are 3" or using a cookie cutter, cut out shapes.
Allow the dough to rise again for about 1 hour.
Pour peanut oil into an electric skillet or a deep frying pan. (2-3 inches) Heat oil to approximately 375 degrees.
Test the temperature of the oil with a small scrap of dough. If the dough begins to fry, the oil is ready. If it turns dark brown too quickly, the oil is too hot.
Make sure to spread the beignets out in the pan. Do not overcrowd the oil. Fry on each side 1-2 minutes.
Remove with a slotted spoon and allow to cool for 1-2 minutes. Sprinkle powdered sugar over the beignets and serve warm.