Combine bread flour, sugar, and salt in a stand mixer bowl.
Beat egg and mix with whole milk, then add yeast to the mixture.
Slowly pour the egg and milk mixture into the flour mixture while mixing until a dough forms.
Knead the dough until smooth, then add shortening or unsalted butter and mix until combined.
Shape the dough into a ball, cover, and let it rise for 45-60 minutes.
Divide the dough into 16 pieces, shape into balls, and let rest.
Roll out each dough piece into a quarter-inch thickness, shape into donuts, and let rise for 20-25 minutes.
Prepare the butter coating by combining all-purpose flour, rice flour, cornstarch, baking soda, and water to make a tempura-like batter.
Coat the donuts with the butter mixture.
Optionally, coat the donuts with a mixture of sugar and powdered milk or kinako.
Deep fry the donuts in vegetable oil at 160 degrees Celsius for 3 minutes on each side.
Drain excess oil on a wire rack and coat with sugar or sugar and powdered milk mixture.
Serve and enjoy the crispy, chewy, and delicious Taiwanese donuts.
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