Prepare the Dough:
In a large bowl, whisk together the glutinous rice flour, tapioca starch, granulated sugar, baking powder, and salt. In a separate bowl, whisk together the milk, vegetable oil, egg, and vanilla extract. Slowly pour the wet ingredients into the dry ingredients, mixing until just combined. The dough will be sticky.

Rest the Dough:
Cover the dough and let it rest for 15-20 minutes to allow the glutinous rice flour to fully absorb the liquid and create a better texture.

Shape the Doughnuts:
Transfer the dough to a piping bag fitted with a large round tip. Pipe 8 small circles, about 1-1.5 inches in diameter, connected in a ring shape on parchment paper. Each circle should touch the next. Repeat the process to make 12 doughnuts. Cut around each doughnut so they are individually on parchment paper squares.

Fry the Doughnuts:
Heat vegetable oil in a deep pot or fryer, about 2-3 inches deep, to 325-350°F (160-175°C). Carefully lower the doughnuts, parchment paper and all, into the hot oil. Fry for 2-3 minutes on each side, or until golden brown and puffed up. The parchment paper will detach after a few seconds. Use tongs to remove the doughnuts from the oil. Place them on a wire rack lined with paper towels to drain excess oil.

Glaze and Decorate:
In a small bowl, whisk together powdered sugar, milk, and vanilla extract to create a smooth glaze. Add food coloring if desired to customize the color. Dip each doughnut into the glaze and let the excess drip off. Optionally, sprinkle with your choice of toppings such as sprinkles, chopped nuts, or chocolate shavings.

Let the Glaze Set:
Place the glazed doughnuts on a wire rack and let them sit for 10-15 minutes for the glaze to set.

Serve:
Serve the mochi doughnuts fresh and enjoy!