Preheat the oven to 350°F. Line a two baking sheets with parchment paper. Set aside.
First, make the apples. Combine the diced apple, brown sugar and cinnamon in a small mixing bowl and stir together until the apples are evenly coated. Set aside.
Next, make the cookies. In a stand mixer fitted with the paddle attachment, beat together the butter and brown sugar on low speed until combined. Gradually increase the speed to medium-high and mix until light and fluffy, about 2 minutes.
Use a silicone spatula to scrape down the sides and bottom of the bowl, then add in the egg and vanilla. Beat on medium-high speed until the mixture is smooth and combined, about 1 minute, scraping down the sides and bottom of the bowl as needed.
Add the flour, baking powder, spices, and salt and beat on low until just combined and no streaks of flour remain, about 30 seconds. Last, add the apple mixture and fold to combine.
Using a 2 ounce cookie scoop scoop level portions of dough into balls, placing them 2 inches apart on the prepared baking sheets.
Bake until the cookies have puffed up and are set and firm around the edges but still somewhat soft in the middle, 12 to 15 minutes.
While the cookies are baking, make the glaze. In a small mixing bowl combine the powdered sugar, maple syrup, milk, and salt. The glaze will be a little thick, but should still be spoonable. If it’s not, add a teaspoon of milk to thin it out.
Spoon the glaze over the hot cookies. Let the cookies set for 10 minutes for the glaze to harden before digging in!