Prepare the pattern: Trace the shape of a round cookie cutter and draw the distance. Set aside. Cut baking paper into square shapes and set aside. Cut the tip of a piping bag and place it in the tall grass.
Make the water roux:Place the sugar, milk, and oil in a small saucepan and heat on low fire until steaming. Add the flour until the mixture turns pasty and smooth. Remove the mixture from the heat and add in the tapioca starch until it forms into a ball. Add a very small amount of the beaten egg. Add a minimal amount and mix and test if the mixture hangs in a V shape. There might be a leftover. The trick is to try each egg’s addition. Adding the whole egg may result in a very loose batter.
Fry the Mochi Doughnuts:Place the dough in the piping bag. Place the see-through baking paper on top of the pattern and squeeze out the dough. Make sure that the dough are touching each other. Using your finger, push the tip of the dough with water.Heat the cooking oil and fry the dough with the baking paper and remove it when the dough is fixed on its form. Turn and fry each side until golden brown.
Glaze
Mix all of the glaze ingredients and add color to them. Dip the cooled doughnut, then add sprinkle immediately. Let the glaze dry before serving.
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Notes
Make sure that the dough is touching each other. This makes the dough keep its form while frying.