Prepare the Batter:

In a large mixing bowl, whisk together the flour, sugar, baking powder, cinnamon, nutmeg, and salt. In another bowl, combine the eggs, milk, melted butter, and vanilla extract. Gradually mix the wet ingredients into the dry ingredients until just combined. Fold in the diced apples.

Heat the Oil:

In a deep frying pan or pot, heat about 2 inches of oil to 350°F (175°C). Use a thermometer to maintain the temperature for even frying.

Fry the Fritters:

Using a large spoon or an ice cream scoop, drop spoonfuls of batter into the hot oil, being careful not to overcrowd the pan. Fry for 2-3 minutes on each side until golden brown. Remove with a slotted spoon and place on a wire rack lined with paper towels to drain excess oil.

Make the Glaze:

In a small bowl, whisk together powdered sugar, milk, and vanilla extract until smooth. Adjust consistency by adding more milk or powdered sugar if needed.

Glaze the Fritters:

Once the fritters have cooled slightly, drizzle or dip them in the glaze. Let the glaze set for a few minutes before serving.