For the Doughnuts: In large bowl, whisk together millet flour, granulated sugar, oat flour, pumpkin pie spice, baking powder, salt, and xanthan gum. In small bowl, stir together pumpkin, eggs, vegetable oil, and orange juice until smooth. Pour pumpkin mixture over dry ingredients and whisk until no lumps remain.
For the Cinnamon-Sugar Topping: In a 9-inch square pan, stir together granulated sugar and ground cinnamon. Place doughnuts in sugar mixture. Carefully turn over. Allow doughnuts to cool in the sugar. When cool, shake off excess sugar. Store doughnuts, covered, on the counter for up to three days.