Pour apple cider into a small saucepan and simmer until reduced to about ¼ cup. Cool completely.
Whisk melted butter, brown sugar, and granulated sugar until smooth.
Add egg, vanilla, and cooled cider reduction and whisk until combined.
In a separate bowl, whisk flour, baking soda, cinnamon, nutmeg, and salt.
Add the dry ingredients to the wet ingredients and mix just until combined.
Fold in the caramel pieces.
Cover and refrigerate the dough for at least 30 minutes.
Preheat oven to 350°F (175°C) and line baking sheets with parchment or silicone mats.
Scoop dough into approximately 1½-inch balls and space them well apart.
Bake for 10–12 minutes, until the edges are set and lightly golden while the centers remain soft.
Cool on the baking sheet for about 5 minutes, then transfer to a wire rack.
Finish with flaky sea salt if desired.