In the bowl of a stand mixer fitted with the paddle attachment, add the gluten-free bread flour, potato starch, granulated sugar, milk powder, instant yeast, baking powder and salt. Mix to combine.

With the mixer running on low, slowly add the water, melted butter and eggs. Increase the speed to medium and mix for 3 minutes. The dough will resemble thick cookie dough, this is normal.

Using an oiled rubber spatula, scrape down the bottom and sides of the bowl. Cover the bowl tightly with plastic wrap and let rise in a warm place for 45-60 minutes.

After the dough has risen, refrigerate it for 20 minutes. (Refrigerating the dough makes it easier to roll out.)

Turn out the dough onto a lightly floured surface and sprinkle with a little gluten-free flour, then roll the dough out until it is ½-inch thick.

Using a donut cutter, cut out the donuts. Re-roll the dough and cut more donuts as needed.

Fill a large heavy-bottomed pot with oil, about 3-4 inches deep. Place over medium heat until a deep-fry thermometer registers 335°F.

Line a large baking sheet with paper towels. Place a wire rack on top.

When the oil is ready, drop a few donuts into the hot oil, being careful to not overcrowd. Cook for 2 minutes, then turn over and cook for an additional 2 minutes or until they are golden brown.

Remove the donuts from the oil and let them drain on the prepared baking sheet. Repeat with the remaining donuts.

In a small bowl, combine the powdered sugar, milk and vanilla. The glaze should be fluid but not runny. It should coat the back of a spoon and drizzle in a slow, steady stream when lifted. Add a few tablespoons of milk if needed to reach the desired consistency.

Let the donuts cool until just warm to the touch before dipping fully in the glaze. Place the glazed donuts on the wire rack so the excess glaze can drip on the sheet pan below.