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, lemon juice, and cinnamon in a small mixing bowl and stir together until the apples are evenly coated. Set aside.
Next, make the cookie dough. 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.
Scrape down the sides and bottom of the bowl, then add in the egg and vanilla. Beat on medium 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 (maybe 15 seconds for me).
Last, add the apple mixture. I give it a quick couple pulses in the mixer, then fold the rest in by hand. Keep the apple bowl for your glaze.
Using your hands, or a spoon, or a 2-ounce cookie scoop, place portions of dough into balls or lumps on the prepared baking sheet, about 2 inches apart.
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 (they usually need closer to 15).
While the cookies are baking, make the glaze. In the same bowl you made the apples in, combine the powdered sugar, maple syrup, milk, salt, and almond extract. Always go light on the milk at first, to make sure you get the right texture. It should be thick, but still spoonable (add a splash more 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!