Preheat oven to 400°F (200°C). Line 2 baking sheets with parchment paper.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter and sugars at medium-high speed until light and fluffy, 2 to 3 minutes, stopping to scrape sides of bowl. Add egg and vanilla, beating well.

In a medium saucepan, heat cider over medium-high heat until thickened and reduced to 2 tablespoons, 10 to 15 minutes. (An instant-read thermometer should read no less than 150°F [65°C].) You can pour the reduced cider into a glass measuring cup to check the volume. (This transfer will also help the foam to subside.) Let cool for 1 to 2 minutes. (It will harden if cooled any longer.) Beat reduced cider into butter mixture.

In a medium bowl, whisk together flour, cinnamon, salt, and baking soda. In a small bowl, toss together apple and lemon juice. With mixer on low speed, gradually add flour mixture to butter mixture, beating just until combined. Stir in apple mixture. Using a 1½-tablespoon spring-loaded scoop, scoop dough into balls (about 25 grams), and place 2 inches apart on prepared pans.

Bake until golden brown but still soft, 8 to 10 minutes. Let cool on pans for 5 minutes. Remove from pans, and let cool completely on wire racks. Using a piping bag or spoon, drizzle Bourbon Glaze onto cooled cookies. Store in an airtight container for up to 3 days.

In a small bowl, whisk together the confectioners’ sugar, bourbon, and apple cider until smooth. Use immediately.