Using a paring or peeling knife, peel, core, and slice apples into small chunks. Place in a medium-sized bowl, and sprinkle with cornstarch. Stir to coat. Set aside.
In a large bowl, combine flour, sugar, baking powder, salt, cinnamon, and nutmeg. Add apple cider, eggs, and melted butter. Whisk together until moistened. Gently fold in apples.
Heat oil in Dutch oven to 350 degrees. Using a large serving spoon, heap portions of batter into hot oil. Press batter lightly with the back of spoon to flatten. Fry fritters two to three at a time, keeping oil temperature between 325-350 degrees. Cook until a deep golden brown, about 2-3 minutes per side. Transfer fritters to wire rack. Repeat for remaining batter.
To Make the Glaze:
In a medium sized bowl, whisk together powdered sugar, apple cider, cinnamon, and nutmeg. Top each fritter with a spoonful of glaze while still warm. Makes about 8 large fritters.
*Unless otherwise indicated, all butter used on this recipe site is salted.