In a small dish, add the warm water, yeast, and sugar. Allow the yeast to sit 10 minutes until it is frothy.
Add your dry ingredients to a bowl and whisk to blend. Pour the yeast mixture, eggs, milk, and butter into the bowl.
Mix the ingredients together to form a soft dough.
Cover the bowl with plastic wrap and allow the beignet dough to rise 45-60 minutes. I like to rise mine in an oven. Preheat your oven to 200º F. Turn it off and put the bowl into the oven. Leave the door cracked open.
Remove the plastic and put a piece of wax paper down. Dust it with gluten free flour and put the dough on top. Roll the dough to ½ inch thickness and use a sharp knife or pizza wheel to cut small 1 inch squares.
Heat the oil in a dutch oven or large cast iron skillet. I use the side burner on my grill for this so my house doesn't smell like hot oil. You want your oil to be 350º F.
Add the squares of beignet dough a few at a time. Cook 1 ½ minutes and flip them over with a slotted spoon. If your oil is too hot, your beignets will get dark on the outside but be raw inside so make sure your oil temperature is no hotter than the 350º F!
Remove the cooked gluten free fried dough pieces and place on a paper towel. The paper towel will absorb the extra oil. Dip the beignets in powdered sugar and toss to coat.