In a mixing bowl, whisk together the all-purpose flour, granulated sugar, baking powder, baking soda, salt, and nutmeg until smooth.

Add the chilled buttermilk, apple cider, and lightly beaten egg to the dry ingredients.

Stir with a small rubber spatula or spoon until the dough just comes together.

Using a 1-ounce ice cream scoop or 2 tablespoons, scoop and drop 10 balls of dough into the air fryer basket, spaced evenly apart.

Lightly brush the tops of the dough balls with vegetable oil.

Cook the doughnut holes in the air fryer at 350°F (175°C) until they are golden brown and fluffy, about 6 minutes.

Transfer the cooked doughnut holes to a wire rack to cool completely.

In a small bowl, stir together the powdered sugar, unsweetened applesauce, vanilla extract, and kosher salt until smooth to make the glaze.

Dip the tops of the cooled doughnut holes in the glaze, then let them stand until the glaze sets before serving.

Alternatively, for warm doughnuts, dip the doughnut holes in the glaze immediately after cooking and serve warm.