In the bowl of a stand mixer combine Tapioca Starch (1 cup), Gluten-Free All-Purpose Flour (1 cup), Granulated Sugar (5 tablespoon), Baking Powder (2 teaspoon), and Salt (1/4 teaspoon).
To the dry mixture add Whole Milk (2/3 cup), Unsalted Butter (2 1/2 tablespoon), Egg (1), Distilled White Vinegar (1/2 teaspoon), and Vanilla Extract (1 teaspoon). Mix together until thick and smooth batter forms.
Transfer the dough into a large sealable bag.
Cut parchment paper into 5x5-inch squares and the paper on a tray or baking sheet.
Cut the piping bag with a ¼-inch slit in the corner. Pipe the donuts onto the center of parchment squares.
Smooth the top with milk if needed.
Place the tray in the freezer and chill for at least 20 minutes or until you’re ready to fry.
In a wide frypan over medium high heat, warm Vegetable Oil (3 cup) to 330 degrees F (165 degrees C).
Make the glaze. Combine the Powdered Confectioners Sugar (3/4 cup), Vanilla Extract (1 teaspoon), Corn Syrup (1 tablespoon), Salt (1/4 teaspoon), and Unsalted Butter (1 tablespoon). Add in the Whole Milk (3 teaspoon) one spoon at a time to control the thickness.
Using a spatula place the donut, with parchment paper into the hot oil. Cook for 2-3 minutes on each side until golden brown. The donut will separate from the parchment and then you can fish it out. Once cooked, place on a wire rack to cool.
Place the donut into the glaze, flip and coat the other side.
Garnish with Sprinkles (to taste) and serve.