Preheat your oven to 350°F (175°C).
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In a large bowl, beat the softened butter, granulated sugar, and brown sugar together until light and fluffy.
Add the egg and vanilla extract to the butter mixture and beat until well combined.
Pour in the apple cider and mix until just combined.
Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Scoop tablespoon-sized dollops of cookie dough onto a parchment-lined baking sheet, spacing them about 2 inches apart.
Bake for 10-12 minutes, or until the edges are lightly golden.
Let the cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Once cooled, spread a generous layer of caramel sauce on the flat side of half the cookies and sandwich them with the other half.
Dust with additional cinnamon, if desired, before serving.