In a small bowl, mix together the dried active yeast and caster sugar with warm water around 39 to 40°C (102 to 104°F). Allow this mixture to sit for about 5–10 minutes until it becomes frothy.

In a large mixing bowl, combine tapioca starch, mochiko flour, sorghum flour, oat flour (or buckwheat), rough-ground psyllium husk, xanthan gum, fine sea salt, and baking powder. Whisk these dry ingredients together until thoroughly blended.

Warm the milk slightly and add in the vanilla extract. In a separate bowl, beat the egg until well mixed. Incorporate the warm milk mixture and beaten egg into the bowl of dry ingredients, creating a thick batter.

Pour in the activated yeast mixture and mix everything using a sturdy spatula or dough hook on medium speed for about 5–8 minutes. The dough should be sticky yet pliable.

Transfer the mixed dough to a greased bowl, cover it tightly with plastic wrap, and place it in the refrigerator for 1 to 2 hours.

After chilling, remove the dough and divide it into equal portions. Shape each piece into a ball and gently flatten it slightly. Arrange doughnuts on a lined baking sheet and let them proof for about 1.5 hours.

In a deep frying pan, heat oil to 165-170°C (329-338°F). Carefully place a few doughnuts in the hot oil, frying them for about 2.5 to 3 minutes per side or until golden brown.

Transfer doughnuts to a paper towel-lined plate to drain excess oil. While still warm, toss in caster sugar mixed with ground cinnamon if desired. Fill each doughnut with your choice of seedless jam or filling.