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1
Place 2 1/2 cups of flour, the cinnamon, salt, and nutmeg in a large bowl and whisk to aerate and combine; set aside.
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2
Coat a second large bowl with vegetable oil; set aside.
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3
Place the yeast and 1 teaspoon of the sugar in a medium bowl.
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4
Heat 1/2 cup of the apple cider until warm, between 105 degrees F and 115 degrees F. Add to the yeast and sugar and stir to combine.
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5
Let sit until the mixture is foaming, about 5 minutes.
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6
Add the remaining 1/4 cup sugar, remaining 1/4 cup apple cider, egg yolks, apple butter, and vanilla to the yeast mixture and whisk to combine.
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7
Add this mixture to the reserved flour mixture and stir with a wooden spoon until the dough comes together and begins to form a ball.
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8
Transfer the dough to a lightly floured work surface.
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9
Scatter the butter pieces over the dough and knead until the butter is fully incorporated and the dough is smooth, shiny, and elastic, about 6 to 8 minutes.
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10
Add up to 1/4 cup of additional flour as needed if the dough is sticky.
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11
Form the dough into a ball, place it in the oiled bowl, and turn to coat it in the oil.
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12
Cover the bowl with plastic wrap or a damp towel and let the dough rise in a warm place until doubled in size, about 2 hours.
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13
Meanwhile, make the filling.
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14
Combine the sugar, water, and salt in a medium saucepan and bring to a boil over medium heat, stirring often until the sugar has completely dissolved.
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15
Continue to boil, swirling the pan occasionally (but not stirring), until the mixture turns a deep amber color, about 10 to 15 minutes.
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16
Remove the pan from the heat, carefully pour in the cream and vanilla (the mixture will bubble up and steam), and stir until evenly combined.
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17
Transfer to a medium heatproof bowl and let the caramel cool at room temperature, uncovered, for about 30 minutes before using.
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18
Line a baking sheet with parchment paper; set aside.
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19
Punch down the dough, transfer it to a lightly floured work surface, and roll it out until its about 1/4 inch thick.
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20
Using a 2-1/2-inch round cutter, stamp out as many dough rounds as possible and place them on the prepared baking sheet about 1/4 inch apart.
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21
Gather the dough scraps into a ball and roll out and cut again.
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22
Discard any remaining dough scraps.
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23
Cover the dough rounds loosely with plastic wrap or a damp towel.
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24
Let rise in a warm place until puffy and about 1/2 inch thick, about 30 minutes.
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25
Heat the oil in a Dutch oven or a large, heavy-bottomed pot over medium heat until the temperature reaches 365 degrees F on a candy/fat thermometer.
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26
Meanwhile, fit a wire rack over a second baking sheet; set aside.
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27
Place the sugar in a large bowl; set aside.
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28
Transfer the cooled caramel to a piping bag fitted with a 1/4-inch round tip; set aside.
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29
When the oil is ready, add 4 of the dough rounds and fry until golden brown, flipping halfway through, about 2 minutes total.
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30
(If air bubbles appear in the donuts, pierce them with the tip of a paring knife.)
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31
Remove the donuts with a slotted spoon to the rack.
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32
Add 4 more dough rounds to the oil.
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33
While these dough rounds are frying, use tongs to transfer the first 4 (still-hot) donuts to the bowl of sugar.
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34
Toss to coat in the sugar, then return to the wire rack.
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35
Repeat frying and sugarcoating the remaining dough rounds.
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36
When the donuts are cool enough to handle, use a paring knife to puncture the side of each to form a pocket in the center.
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37
Place the tip of the piping bag into the pocket and pipe about 1 heaping teaspoon of caramel inside.
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38
Serve warm or at room temperature.
