Caramel Apple Cookies

Arrange oven racks in upper third and middle positions; preheat to 350 degrees F. Line 3 baking sheets with parchment paper. Beat brown sugar and butter in a large bowl with an electric mixer on medium speed until light and fluffy, 3 to 4 minutes. Add egg; beat until fully incorporated, about 30 seconds. Add vanilla; beat until incorporated, about 15 seconds.

Whisk flour, baking soda, salt and apple pie spice together in a medium bowl. Gradually add the flour mixture to the butter mixture alternately with milk, beginning and ending with the flour mixture and beating on low speed until just combined after each addition. Gently fold in apples.

Scoop the dough using a 1 1/2-inch cookie scoop (or by rounded tablespoonfuls) and arrange 2 inches apart on the prepared baking sheets. Bake 2 of the pans until the cookies are browned on the bottoms and set, 12 to 14 minutes, rotating the pans between the top and middle racks halfway through the baking time. Let the cookies cool on the pans for 5 minutes. Transfer the cookies to a wire rack and let cool completely, about 20 minutes. Meanwhile, repeat the process with the remaining pan, using the middle oven rack.

Place caramel candies and water in a small microwaveable bowl. Microwave on High until completely melted and smooth, about 1 minute, stirring after 30 seconds. Drizzle the warm caramel mixture over the cooled cookies. Let stand at room temperature until the caramel is set, about 15 minutes (or chill until set, about 5 minutes).