Prepare the oven: Heat the oven to 375°F (190°C) and line a baking sheet with parchment paper.
Mix the dry ingredients: Whisk the flour, sugar, baking powder, cinnamon, nutmeg, and salt in a large bowl.
Mix the wet ingredients: Whisk the eggs, milk, vanilla, and melted butter in a separate bowl.
Make the batter: Stir the wet mixture into the dry ingredients just until combined. Fold in the diced apples.
Bake: Scoop the batter onto the baking sheet and bake for 18 to 22 minutes, until puffed and lightly golden.
Make the glaze: Whisk the powdered sugar, cinnamon, vanilla, and milk until smooth and pourable.
Finish: Cool the fritters for five minutes, drizzle with glaze, and let set for about ten minutes.