In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg. In a separate large bowl, combine the melted butter, light brown sugar, and applesauce. Whisk in the vanilla extract and eggs until well mixed. Gradually add the dry ingredients to this mixture, stirring until smooth. The batter will be quite thick. If necessary, pour in the milk halfway through mixing to help loosen the batter.