If your kids are like mine, they will want to watch these doughnuts puff up in the oil. Let them peek over your shoulder, safely away from the hot pan. Put them to work cutting out the doughnuts, and then let them shake the warm doughnuts with the cinnamon sugar in a paper bag that they’ve decorated themselves.

Steps

1. Pour the oil to a depth of at least 1 inch into a deep, heavy pot and heat to 375 degrees on a deep-frying thermometer. Make sure the pot is no more than half full. Put a large rack on a large rimmed baking sheet and place near the stove.
2. Meanwhile, in a bowl, stir together the flour, sugar, salt, baking soda, baking powder, and nutmeg. In another bowl, whisk together the egg, buttermilk, cider, melted butter, and vanilla until smooth. Add the egg mixture to the flour mixture and stir until the dough is thick.
3. With floured hands, transfer the dough to a floured work surface, and knead lightly until the ingredients are evenly mixed. The dough will be loose and sticky. Pat the dough into a round 1 inch thick. Flour a doughnut cutter 2¼ inches in diameter and cut out the doughnuts, flouring the cutter as needed to prevent sticking. Or, use 2 round cutters, 2¼ inches and 1¼ inches in diameter. Scraps can be patted into a disk and cut again.
4. Using a flat spatula, carefully slide the doughnuts and holes, 2 or 3 at a time, into the hot oil and fry until golden on the undersides, about 1 minute. Using a slotted spoon, flip them over and fry on the other side until golden, 1 to 2 minutes. If darkening too quickly, reduce the heat slightly. With the spoon, transfer to the rack(s) to drain.
5. While the doughnuts are still warm, put the cinnamon sugar in a paper bag, add the doughnuts, and shake gently to coat. Enjoy!