Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper or lightly grease it.
In a large bowl, whisk together the flour, granulated sugar, baking powder, salt, cinnamon, and nutmeg.
In another bowl, whisk together the eggs, milk, vanilla extract, and melted butter until smooth.
Gradually add the wet ingredients to the dry ingredients, stirring gently until just combined.
Fold in the diced apples until they are evenly spread throughout the batter.
Scoop heaping spoonfuls of batter onto the prepared baking sheet, keeping about 2 inches apart.
Bake for 14–16 minutes or until the fritters are golden brown and a toothpick comes out clean.
While the fritters cool slightly, whisk together the powdered sugar, milk, and vanilla extract for the glaze until smooth.
Drizzle or brush the glaze over the warm fritters. Let it set for a few minutes before serving.