In a large bowl, whisk together the egg, milk, sugar, salt, vanilla, cinnamon, and nutmeg.
Stir in the apples.
Add sifted flour and fold in just until combined.
Pour 3-4 inches worth of oil into a Dutch oven. Heat to 350 degrees. For best results, use a deep fry or candy thermometer attached to the side of the pan to monitor temperature.
Use a spoon or small ice cream scoop to carefully (without splashing oil) drop heaping tablespoons of batter into oil. If using a spoon, use a second spoon to scrape the batter into the oil.
Fry until they develop a deep golden brown color, turning once. They will need to cook about 2-3 minutes per side. To test that they are done, remove one from the oil and split it open. If there is still wet batter in the middle, they need to cook longer.
Place on a cooling rack set on top of a baking sheet.
Notes
Recipe adapted from Craftsy Simple to Sensational Doughnuts