Preheat the oven to 375°F (190°C). Line a large baking sheet with parchment paper so the fritters do not stick and clean up is easy.
In a large bowl, whisk the flour, granulated sugar, baking powder, cinnamon, nutmeg, and salt until evenly combined and no spice clumps remain.
In a medium bowl, whisk the milk, eggs, vanilla, and melted butter until smooth. If the butter is very hot, let it cool a few minutes so it does not scramble the eggs.
Pour the wet mixture into the dry mixture. Stir gently with a spatula just until the flour disappears. The batter will look thick and a bit lumpy, which is perfect. Overmixing makes the fritters dense.
In a small bowl, toss the diced apples with brown sugar and cinnamon until coated. Dice the apples small so they soften evenly while baking.
Fold the apple mixture into the batter with 6 to 8 gentle turns until the apples are evenly distributed.
Scoop the batter into 10 to 12 mounds on the prepared baking sheet. Leave space between each one. If you want a more classic fritter shape, make slightly uneven mounds rather than perfectly smooth scoops.
Bake for 22 to 25 minutes, or until the tops are lightly golden and the centers feel set when gently pressed. If your fritters are large, add 2 to 3 minutes.
Cool the fritters on the baking sheet for 5 minutes, then transfer to a rack if you have one. This helps the bottoms stay tender instead of soggy.
For the glaze, whisk powdered sugar, milk, and vanilla until smooth. Drizzle over warm fritters for a thin glaze, or wait until completely cool for a thicker finish.