Prepare the Wet Ingredients: In a standing mixing bowl, crack open the 2 eggs and beat them with 1¼ cup of sugar until well-combined and slightly frothy, about 2 minutes. Next, add in 1 cup of whole milk, 1 cup of sour cream, 1 teaspoon of gluten-free vanilla extract, and 5 tablespoons of softened melted butter. Mix until all the ingredients are fully incorporated and smooth.

Mix the Dry Ingredients: In a separate bowl, whisk together 5 cups of gluten-free all-purpose flour, 2 teaspoons of baking soda, 1½ teaspoons of gluten-free baking powder, 1½ teaspoons of salt, and 2 teaspoons of xanthan gum. Make sure to break up any clumps in the flour.

Combine Wet and Dry Ingredients: Gradually add the dry mixture into the bowl of wet ingredients, stirring continuously with a spatula until just combined. Avoid over-mixing to ensure your gluten-free donuts remain light and fluffy.

Shape the Donuts: Lightly flour your work surface and turn the dough onto it. Roll out the dough to about 1 inch thick. Using a donut cutter or two different-sized round cookie cutters, cut out donut shapes.

Heat the Oil: In a deep fryer or a large, heavy-bottomed pan, heat oil to 375°F. Use a cooking thermometer to monitor the temperature.

Fry the Donuts: Gently place the donuts into the hot oil, frying them for about 2-3 minutes on each side until golden brown. Use a slotted spoon to flip them halfway through.

Drain the Donuts: Remove the donuts from the oil using a slotted spoon and transfer them to a wire rack set over paper towels to drain excess oil.

Prepare the Glaze: In a bowl, whisk together ½ cup of powdered sugar, 1 tablespoon of milk, and 1 tablespoon of melted butter until smooth and slightly thick.

Glaze the Donuts: Dip the top of each warm donut into the glaze, allowing any excess to drip off. Place them back on the wire rack to let the glaze set.