Position a rack in the center of the oven and preheat to 400°F (205°C). Line a large rimmed baking sheet with parchment paper.

In a large bowl, whisk the flour, granulated sugar, brown sugar, baking powder, cinnamon, nutmeg, and salt until the brown sugar is evenly dispersed and no compact lumps remain.

In a medium bowl, whisk the milk, egg, and vanilla until smooth. Slowly whisk in the melted butter until evenly combined, with no visible layer of butter.

Pour the wet mixture into the dry ingredients. Fold with a rubber spatula just until only a few dry streaks remain. Add the diced apple and fold until evenly distributed and no dry flour remains. Stop mixing as soon as the thick, scoopable batter holds its shape.

Divide the batter into 12 portions of about 1/4 cup each, spacing them at least 2 1/2 inches apart on the prepared baking sheet. With lightly dampened fingers or the back of a small spoon, shape each portion into a compact ring about 3/4 inch thick with a 1-inch opening in the center. Keep the edges rustic and avoid spreading the batter too thinly.

Bake for 10 to 13 minutes, rotating the pan front to back after about 7 minutes if the oven browns unevenly. The fritters are ready when the edges and bottoms are golden, the tops no longer look wet, and the centers spring back lightly when touched. Transfer to a wire rack and cool for 5 minutes before glazing.

Whisk the powdered sugar, 1 1/2 tablespoons milk, vanilla, and salt until smooth. The glaze should fall from the whisk in a thick ribbon that settles back into the bowl within a few seconds. Add more milk 1/2 teaspoon at a time only if needed.

Dip or spoon glaze over the tops while the fritters are warm but no longer steaming heavily. Return them to the wire rack and let the glaze set for about 10 minutes before serving.