Reduce the cider: In a small saucepan, bring 1 1/2 cups of pure apple cider to a brisk simmer over medium heat. Cook for 15-20 minutes until reduced down to exactly 1/3 cup of intensely concentrated syrup. Let cool completely to room temperature.

Mix dry ingredients: In a medium bowl, whisk together the flour, baking soda, baking powder, ground cinnamon, nutmeg, allspice, and fine salt.

Mix wet ingredients: In a large bowl, whisk together the melted butter, dark brown sugar, granulated sugar, cooled apple cider reduction, whole egg, egg yolk, and vanilla extract until completely smooth and emulsified.

Combine & chill: Fold the dry ingredients into the wet mixture using a rubber spatula just until no dry flour streaks remain. Cover the bowl and chill in the refrigerator for 30 minutes to firm up.

Shape & roll: Preheat oven to 350°F (175°C) and line two large baking sheets with parchment paper. Mix 1/3 cup sugar and 1 tsp cinnamon in a small bowl. Scoop 2-tablespoon portions of chilled dough. Flatten slightly, wrap around a soft caramel square, seal tightly into a smooth ball, and roll completely in cinnamon sugar.

Bake & finish: Arrange dough balls 2 inches apart on baking sheets. Bake for 11 to 13 minutes until edges are set and golden and tops are beautifully crinkled. Immediately sprinkle with flaky sea salt and drizzle with warm melted caramel. Cool on pan for 10 minutes, then transfer to a wire rack.