Add the white rice flour, tapioca flour, corn starch, brown rice flour, xanthan gum, baking powder, salt, and nutmeg to a bowl. Using a Wisk, combine the ingredients.
In a separate bowl, add the sugar and unsalted butter. Using a stand-alone mixer, with the paddle attachment, at medium-high speed, beat the butter and sugar until light and fluffy (2-3 minutes). Then, reduce the speed and add the egg, yolk, buttermilk, and vanilla extract. Beat the ingredients until combined (1-2 minutes). Now, slowly add the flour mixture and beat the ingredients until combined (2-3 minutes).
Cut a piece of plastic wrap and place it on your working surface. Dust the plastic wrap with gluten-free flour, then transfer the donut dough to the plastic wrap. Dust the top of the dough with gluten-free flour, then using a rolling pin, roll the dough into a thick disc. Wrap the dough with plastic wrap, and allow it to chill in the fridge for one hour.
Meanwhile, prepare the vanilla sugar glaze while the dough chills. In a bowl, add the powdered sugar, full-fat milk, and vanilla extract. Using the whisk, combine the ingredients and set the glaze aside for later.
Now, transfer the dough to a dusted working surface and roll the dough into a 1.5 cm (½ inch) thick rectangle or circle using a rolling pin. Using a 6 cm ( 2.5 inch) cookie cutter, press into the dough. Then, press a cupcake corer into the middle of the cut-out dough to create the donut hole. Remove the donut hole and set it aside. Transfer the cut-out donut to a baking tray aligned with parchment paper. Repeat until you are out of dough. You can also make bite-sized donuts from the donut holes or any remaining dough you have.
Using a knife, gently score the top of each donut four times to create a rectangle. This will allow the donut to cook evenly and create texture.
In a cooking pot, add the vegetable oil and allow it to get hot. Measure the oil temperature using a thermometer, and once a temperature of 175-180°C (347-356°F) is reached, add three donuts. Cook the donuts for 1-1.5 minutes and then flip them to cook the other side for another 1-1.5 minutes. Transfer the cooked donuts to a cooling rack and allow them to cool for 5 minutes before dipping them into the glaze to cover them completely.