Preheat deep fryer to 375 degrees.
Combine dry ingredients in a large bowl. Whisk.
Combine rice milk, vanilla and melted butter in a measuring cup.
Add wet ingredients to dry mixture. Mix until combined.
Sprinkle wheat starch on your work surface. Gently roll out or pat dough to about 1/3 inch thickness. Cut with a doughnut cutter, or use two round biscuit cutters of different sizes.
Place donuts in the fridge for at least 10 minutes, up to 30.
Place a few of the donuts into the deep fryer. Fry until golden brown, about 3 to 5 minutes, flipping once
Place 1 cup sugar in a brown paper bag and toss the doughnuts in to cover. Serve warm or at room temperature.
Variations: Cinnamon Sugar: add 1 teaspoon cinnamon to the sugar and toss. Glazed donuts: combine 3 cups powdered sugar, 1/2 cup rice milk and 1/4 teaspoon vanilla together to make glaze. When the doughnuts have cooled, dip both sides of each doughnut into the glaze, shake off any excess glaze, and transfer to a wire rack to set the glaze.