In a small pot, bring the apple cider to a simmer over medium heat. Stir in the apple pieces and the brandy and remove from the heat. Cover and let the apples soak for at least 30 minutes or up to 3 hours.

Drain the apples through a fine mesh sieve, gently pressing them with the back of a spoon to release extra liquid. Reserve the soaking liquid for the glaze.

In a small saucepan, melt the butter over medium heat. Continue cooking until the solids have separated and turned brown, 6 to 8 minutes. Transfer to a medium bowl. Whisk in the cinnamon, ginger, all-spice, and vanilla into the browned butter, and let the spices bloom for 5 minutes. Whisk in the orange and lemon zest.

Add the brown sugar, ¼ cup granulated sugar (50g), and egg, and whisk until well combined. Stir in the apples.

In a large bowl, combine the flour, baking soda, baking powder, and salt.

Pour the butter mixture into the flour mixture and stir together with a spatula until just combined. Refrigerate the dough for 30 minutes.

Meanwhile, preheat the oven to 350°F. Line two large baking sheets with parchment paper.

Scoop the dough into 2 tablespoon-sized balls (about 40g) and roll in the remaining ¼ cup (50g) of granulated sugar. Place them on the prepared baking sheets about 2 inches apart.

Bake one sheet at a time until the edges are set and the centers appear dry but are not firm to the touch, 10 to 12 minutes. Let the cookies cool on the pan for 5 minutes, then transfer to a wire rack to cool completely.

In a medium bowl, whisk together the confectioners’ sugar and 3 tablespoons of reserved apple-soaking liquid until smooth. If the icing is too thick, add the additional 1 tablespoon of soaking liquid, 1 teaspoon at a time.

Drizzle the icing over the top of the cooled cookies. Let the glaze set for at least 30 minutes, or until hardened and dry, before serving or storing.