Preheat oven to 350°F. Grease donut pan.
In a large bowl, whisk together flour, xanthan gum, corn starch, baking powder, baking soda, salt, nutmeg, and sugar.
Create a well in the middle of ingredients. Add butter, eggs, Greek yogurt, and vanilla. Mix until just combined.
Fill donut pan until almost full, using a piping bag if desired. A trick to help them keep their shape is to wet your pointer finger and run around the batter, pushing it towards the donut perimeter.
Bake in center of the oven for 12 minutes or until slightly browned. Cool in pan for 5 minutes then transfer to wire rack.