Preheat the oven to 180C / Fan 160C / Gas 4 and grease two, 6-hole doughnut tins well with a little oil. (See notes if using a muffin tin instead)
Add the gluten free flour, sugar, cinnamon and baking powder to a large mixing bowl and stir together with a wooden spoon.
In a separate bowl, add the milk, oil, egg and vanilla extract and gently whisk together until combined.
Pour the liquid ingredients into the dry ingredients and use a whisk to mix together until it forms a runny batter with no lumps.
Pour the batter evenly between the doughnut moulds (approx 2 tbsp per hole) making sure the 'hole' in the middle isn't covered. If you get batter on this bit, wet your finger with a little cold water and use that to clean it off.
Bake the doughnuts in the oven for 12-15 minutes until well-risen and golden brown on top. Remove from the oven and place the tins on a cooling rack while you make the sugar coating.
Add the granulated sugar and cinnamon to a tub, place the lid on firmly and shake to mix. Pour out onto a large plate.
Use a knife to carefully remove the doughnuts from the tin. One at a time, brush the doughnuts with melted butter using a pastry brush, then coat in the cinnamon sugar. Repeat until all coated.
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Notes
If Using A Muffin Tin: Grease the tin well and add approx 2 tbsp of batter per well. Bake for 12-15 minutes until golden - you may find they need nearer 15 minutes due to the lack of hole in the middle!
No Self-Raising Flour? Add 1.25 tsp extra gluten free baking powder and 0.25 tsp xanthan gum to a plain gluten free flour blend. Mix well before adding to the recipe.