In a stand mixer fitted with the paddle attachment, beat together the butter, brown sugar, and maple syrup on low speed until combined. Gradually increase the speed to medium-high and beat 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, vanilla, and maple extract. Beat on medium-high until the mixture is fluffy and lightens in color, about 2 minutes, scraping down the bowl as needed.
Stop the mixer, then add the flour, salt, baking soda, baking powder and spices, and beat on low speed until just combined and no streaks of flour remain.
Use a 1 ½ ounce cookie scoop to scoop out equal amounts of dough and roll into balls. Place the dough on the prepared baking sheets, spacing the balls out 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 14 minutes. Remove the baking sheet from the oven and allow the cookies to cool completely.
While the cookies cool, make the maple glaze. Combine the confectioners’ sugar, milk, maple syrup, vanilla and salt in a small mixing bowl and whisk to combine. Whisk until smooth. Drizzle the cookies with the glaze and top with flaky salt if desired! Enjoy!