In a medium bowl, whisk together the flour, brown sugar, baking powder, cinnamon, nutmeg, and salt.
In a small bowl or measuring cup, whisk together the milk, melted butter, egg, and vanilla extract.
Add the wet ingredients to the dry ingredients and mix until just combined. Do not over-mix.
Gently fold in the grated apple, then let the batter sit for at least 5 minutes to thicken.
Preheat a skillet over medium heat and lightly grease with butter, oil, or non-stick spray.
Use a 1/4 cup scoop or 1/3 cup measuring cup to drop the batter onto the skillet.
Cook for 1-2 minutes until small bubbles form on the surface, then flip. Cook for another 1 minute or until golden brown.
Transfer cooked pancakes to a baking sheet and keep warm in a 200°F oven if desired.
Repeat with the remaining batter, adding more butter or oil to the skillet as needed.
For the vanilla maple syrup, whisk together the maple syrup and vanilla extract. Warm in the microwave and serve over the pancakes.