In a large bowl, whisk together the flour, granulated sugar, baking powder, cinnamon, nutmeg, and salt.

In a separate medium bowl, whisk the egg, then stir in the milk and melted butter.

Pour the wet ingredients into the dry ingredients and mix until just combined. Gently fold in the diced apples. Do not overmix the batter.

In a heavy-bottomed pot or Dutch oven, heat about 2 inches of oil over medium-high heat until it reaches 350°F (175°C).

Drop rounded tablespoons of the batter into the hot oil, frying in batches of 3-4 at a time. Do not overcrowd the pan.

Fry for about 2-3 minutes per side, until golden brown and cooked through. Use a slotted spoon to transfer the fritters to a wire rack placed over a baking sheet to drain excess oil.

While the fritters cool slightly, prepare the glaze. In a small bowl, whisk the powdered sugar, 2 tablespoons of milk, and vanilla extract (if using) until smooth. Add more milk, one teaspoon at a time, until you reach your desired consistency.

Dip the top of each warm fritter into the glaze or drizzle it over them. Allow the glaze to set for a few minutes before serving.