Put ¼ cup of flour (bread flour or all purpose flour) into the pot. Pour ¾ cup of water. Mix it very well.
Turn on medium small fire. Keep stirring until the mixture becomes thickened. Then, put it aside and let it cool off.
Pour ½ cup of milk (warm or room temperature) into the Bosch mixer.
Next, add 4 tablespoons of sugar, 3 tablespoons of butter (softened), 1 large egg and 2 teaspoons of active dry yeast into the Bosch mixer.
Turn on the Bosch mixer to # 1 the lowest setting. Let it mix a little bit and wait for 5 minutes.
In the meanwhile, put 2.5 cups of flour (bread flour or all purpose flour) into the bowl and add ½ teaspoon of salt. Mix it well.
After that, turn on the mixer to #1 the lowest setting. Slowly add the flour mixture from step 6 into the yeast mixture. Let it mix a little bit. Then, add the warm tangzhong from step 2. ( Remember the tangzhong needs to be cool off. Not too hot, just a little warm.)
After, change the Bosch mixer speed to #3 the medium high speed setting. Let the mixer run for 8-10 minutes.
Put the dough into a bowl and cover with a wet cloth. Let it rise for 45 minutes to an hour at room temperature. (To speed up the rising time. Normally, I preheat the oven for 200F. Then, turn off the oven and put the dough in for 30 minutes.)
The dough rises its double size.
Roughly divide the dough into 12 pieces.
Roll the dough into a ball shaped.
Take a ball shaped dough, use your palm to press the dough.
Use a small circle cutter, put in the middle of the flatten dough and cut the middle part out. Repeat step 13 and 14 for the rest of the dough.
Cover the doughnut dough with wet cloth. Let it rise for 30 minutes at the room temperature. (To speed up the rising time. Normally, I preheat the oven for 200F. Then, turn off the oven and put the dough in for 15 minutes.)
While waiting for doughnut dough to rise, pour 2 cups of vegetable oil into the wok. Turn on a small fire, heat up the oil temperature around 360-375F. You can use a thermometer or wooden chopsticks to test the temperature. When you put the wooden chopsticks into the oil, if there are little bubbles around the chopsticks. It's a sign to show that the oil is hot enough.
Slowly put the dough into the oil and deep fry for around 1 minute. Then, flip the other side and deep fry for around 1 minute.
Repeat step 17 until all the dough is deep fried.
Lastly, put ¼ cup of sugar on a plate. Then, put the deep fried doughnuts on the plate. Cover and dust the doughnuts with sugar.