Start preheating the oil before you make the donut hole batter. Make sure that your oil is at least 2 inches (5cm) deep in whatever saucepan or pot you're using. Heat the oil to 355-365ºF (180-185ºC). You need to maintain this oil temperature throughout the frying process, so adjust the heat as necessary.
In a large bowl, whisk together the yoghurt, sugar, egg, melted butter and vanilla until well combined and smooth.
In a separate bowl, whisk together the tapioca starch, millet flour, sorghum flour, baking powder, xanthan gum and salt.
Add the dry ingredients to the wet and mix everything together into a smooth, fairly thick batter with no flour clumps. It should have the consistency of thick cake batter.
Once the oil has reached 355-365ºF (180-185ºC), drop about 1½ tablespoon portions of the batter into the hot oil. You should get 18-20 donut holes in total.
Fry the donut holes for about 4-5 minutes in total, flipping them every 30-45 seconds to ensure an even, deep golden brown colour.
Use a skimmer (spider strainer) or a slotted spoon to remove the donut holes from the oil onto a baking sheet lined with paper towels.
In a large bowl, mix together the sugar and cinnamon.
Allow the hot donut holes to cool for about 5 minutes, then roll them in cinnamon sugar.
Serve warm.
