Simmer apple cider in a saucepan over medium heat until reduced to 1/2 cup and let cool.
Preheat oven to 350°F and line two baking sheets with parchment paper.
In a medium bowl, whisk together the flour, baking soda, salt, cinnamon, ginger, and nutmeg.
In a large bowl, cream together the brown sugar and vegetable oil until smooth.
Add the egg and vanilla extract to the oil mixture, beating until well combined.
Alternately add the flour mixture and cooled cider reduction to the wet ingredients, mixing until just combined.
Drop rounded tablespoons of batter onto prepared baking sheets, spaced 2 inches apart.
Bake for 12 minutes or until the tops spring back when lightly touched.
Let cakes cool completely on a wire rack.
While cooling, beat the butter, powdered sugar, and maple extract until creamy to make the filling.
Pipe or spread the filling onto the flat side of half the cooled cakes and top with the remaining halves.