Mix the diced apples with brown sugar, cinnamon, lemon juice, and a pinch of salt in a medium bowl. Let the mixture sit for 10 minutes, allowing the apples to release their natural juices and absorb the flavors.
In a large bowl, whisk together the flour, sugar, baking powder, salt, cinnamon, and nutmeg until well combined.
In a separate bowl, beat the eggs lightly, then add the milk, melted butter, and vanilla extract.
Pour the wet ingredients into the dry ingredients and stir just until combined – a few small lumps are perfectly fine! Avoid overmixing.
Fold the apple mixture, including any juices, into the batter until evenly distributed.
Heat your cast iron skillet over medium heat and add enough oil to cover the bottom with about 1/4-inch depth. The perfect temperature is around 350°F.
Using a 1/4-cup measuring cup or ice cream scoop, drop portions of batter into the hot oil, being careful not to overcrowd the pan (3-4 fritters at a time works best).
Cook for about 2-3 minutes until golden brown on the bottom, then flip carefully and cook for another 2 minutes.
Transfer cooked fritters to a paper towel-lined plate to drain excess oil. Continue with remaining batter, adding more oil to the skillet as needed between batches.
To make the optional glaze: Whisk together powdered sugar, milk or cider, and vanilla extract until smooth. Adjust consistency as needed.
Drizzle glaze over the warm (not hot) fritters or dip the tops directly into the glaze. Serve warm.