Gluten-free doughnuts

I miss my donuts. I have tried, rather unsuccessfully, to duplicate yeast
glazed donut. They usually turn out with a muffin-like texture and have a
gritty aftertaste.
I have had some success with Blue Chip Group's Scone Mix,(now called
Auguson Farms) but was looking for something I could make with the flours I
keep on hand. I think this recipe is the closest I have come, with out actually using AP flour..lol..

Now onto the recipe:

1 packet yeast(2 tsp)
1/8 cup warm water
3/4 cups lukewarm milk
1/4 cups sugar
1/2 tsp salt
1 egg
3 Tbs shortening, melted
1 3/4 cups GF flour mix
1 1/2 tsps xanthan gum
vegetable oil for frying

Combine 1 3/4 cups flour with xanthan gum, set aside. Dissolve yeast in warm water . In a 2 1/2-quart bowl add milk, sugar, salt, eggs, shortening and 1 1/2 cups of flour with xanthan gum mixed. Add yeast mixture, and beat on low speed, scraping bowl. (about 30 seconds). Beat on medium speed, scraping bowl occasionally (2 minutes). Turn dough onto well floured surface. Gently roll dough 1/2 inch thick with floured rolling pin, or pat with hands. Cut with a floured doughnut cutter. Cover and let rise until doubled (40-50 minutes). Heat the vegetable oil in a deep fryer to 350F. Fry until golden brown, about 2 minutes each side.