Pour apple cider into a saucepan and bring it to a boil over medium-high heat. Continue simmering until the liquid has reduced to one-quarter of its original volume. Measure 1 tablespoon for the recipe and allow it to cool completely before use. If prepared in advance, keep the reduction refrigerated.
Place the unsalted butter in a saucepan over medium heat and allow it to melt. Continue cooking while occasionally swirling the pan until toasted brown milk solids develop on the bottom and the butter gives off a distinctly nutty aroma. Immediately transfer the browned butter to a heatproof container. Refrigerate until it becomes semi-firm and resembles a loose, spreadable paste rather than solid butter.
Preheat the oven to 350°F (175°C). Place the cooled browned butter and packed dark brown sugar in a large mixing bowl. Beat with an electric mixer at medium-high speed for approximately 1 minute, until thoroughly blended.
Add the maple syrup, apple butter, 1 tablespoon of cooled reduced cider, room-temperature egg yolk, and vanilla bean paste or extract. Continue mixing until the ingredients form a smooth, cohesive base.
In a separate bowl, whisk together the all-purpose flour, fine sea salt, baking soda, baking powder, cinnamon, nutmeg, allspice, and ginger until evenly distributed.
Gradually mix the dry ingredients into the wet mixture at low speed, stopping as soon as the flour mixture has been incorporated. Using a wooden spoon or similar utensil, gently fold in the chopped white chocolate until it is dispersed throughout the dough.
Line two baking sheets with parchment paper. Divide the cookie dough into 16–18 portions and roll or scoop them into balls. Arrange the portions approximately 2 inches apart on the prepared baking sheets.
Bake for 9–11 minutes. The cookies should appear puffed and soft, with centers that still look slightly underdone when removed from the oven.
Leave the cookies on the baking sheets for several minutes so they can continue setting from the residual heat. Transfer them afterward to a wire cooling rack and allow them to cool completely.
Once the cookies have fully cooled, drizzle 2–3 tablespoons of maple cream across their tops.
For the alternate topping, whisk 1/2 cup confectioners' sugar with 1 tablespoon of the reduced apple cider until a smooth glaze forms. Drizzle the glaze over the cooled cookies using a fork or piping bag.