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1
In a saucepan set over medium heat, warm the milk and butter until the butter just melts.
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2
Put the starter and flour in the bowl of an electric mixer fitted with the paddle attachment and mix on medium-low speed.
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3
Add the milk and butter, followed by the sugar, egg, salt, and yeast.
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4
Finally add the vanilla extract and knead the dough until it is soft and slightly tacky.
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5
Grease a large bowl with butter and place the dough inside, turning to coat with butter.
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6
Cover with plastic wrap.
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7
Let rise for 6 hours at room temperature.
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8
Using a rubber spatula, gently loosen the dough from the bowl.
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9
Dampen your hands with cool water and, with the dough still in the bowl, slide one hand under one side of the dough.
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10
Fold that side of the dough into the center and press down gently so the dough adheres to itself.
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11
Give the bowl a quarter turn and repeat the folding process.
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12
Do this two more times.
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13
After the fourth fold, flip over the dough so the seams are on the bottom.
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14
Cover the bowl with plastic wrap and let the dough rise a second time for 8 to 12 hours at room temperature.
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15
Dust a work surface with flour and turn the dough out onto the flour.
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16
Lightly dust the top of the dough with more flour and pat it out so it is roughly 1/2 inch (1.25 centimeters) thick.
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17
Use a doughnut cutter or two different-sized round cutters to cut out a dozen doughnuts.
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18
You may be able to cut out a few extra holes.
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19
(Roll and cut the dough only once.
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20
You can fry the irregular cuttings for kitchen snacks.)
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21
Separate the doughnuts from the holes and lay them all on a lightly floured baking sheet.
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22
Fill a heavy-bottomed pot halfway with rice bran oil and heat to 350F (175C).
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23
In a medium bowl, combine the sugar and cinnamon; set aside.
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24
Set a metal rack over a rimmed baking sheet.
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25
When the oil is hot, test it with a doughnut hole or a dough piece.
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26
When the doughnut is golden on one side, use a metal spider or slotted spoon to flip it over.
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27
Set the tester on the rack to drain.
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28
Check the inside of the doughnut for doneness.
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29
Once the test doughnut is cooked, proceed with the doughnut holes.
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30
Cook the doughnuts 3 or 4 at a time so the oil temperature does not fluctuate too much.
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31
Fry the doughnuts for 2 minutes on one side.
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32
Flip them over and fry for 2 to 3 more minutes or until golden brown.
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33
Drain the doughnuts and toss them in the bowl of cinnamon sugar while they are still warm.
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34
Place the sugared doughnuts on a plate and continue cooking the rest.
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35
The doughnuts are best warm but will keep up to 3 days in an airtight container.