In a large mixing bowl, whisk together the eggs and sugar until fully blended. Gradually mix in the whole milk, sour cream, gluten-free vanilla extract, and melted unsalted butter.

In a separate bowl, whisk together the gluten-free all-purpose flour, baking soda, gluten-free baking powder, salt, and xanthan gum.

Gradually add the dry ingredients to the wet mixture, stirring gently to combine until a cohesive dough forms.

On a heavily floured surface, roll out the donut dough to a thickness of about 1 inch. Cut out the donut shapes.

Heat oil to around 375°F (190°C). Carefully drop in the donuts, frying them for 2-3 minutes on one side until golden brown.

While the donuts cool, prepare your glaze by mixing powdered sugar, milk, and melted butter in a bowl. Dip each donut into the glaze.