Take your egg out at least 30 minutes before baking so it reaches room temperature. Measure the remaining ingredients by weight if you can. This small habit keeps the dough thick and the cookies chewy.
Cut the butter into small chunks and melt it in a saucepan over medium heat. Stir constantly until it smells nutty and turns a deep amber color. Watch it closely, because it can burn quickly, then set it aside to cool slightly with one ice cube to replace the lost liquid.
Pour the browned butter into a large bowl and add the brown sugar and granulated sugar. Whisk until everything looks combined. The mixture will not cream like regular cookie dough, and that is perfectly fine.
Whisk in the egg, vanilla extract, and maple extract if you are using it. Keep whisking until the mixture looks smooth and glossy. The maple extract is optional because the drizzle brings plenty of maple flavor later.
Whisk the salt, chai spice, baking powder, and flour in a separate bowl. Stir this into the butter mixture just until no white streaks remain. Cover the bowl and chill it for at least 30 minutes, or up to 24 hours.
Heat the oven to 350°F (176°C) and line two baking sheets with parchment paper. Mix the topping sugar and chai spice in a shallow dish. Scoop rounded mounds of dough, about 2 to 3 tablespoons each, and roll them until fully coated.
Place about eight cookies on each sheet so they have room to spread. Bake for 12 to 14 minutes, until puffy with set edges. The centers will look slightly underbaked, but they firm up as they cool.
Let the cookies cool on the sheet for five minutes, then move them to a wire rack. Meanwhile, whisk the powdered sugar with maple syrup a little at a time. Stop when the glaze flows slowly off the whisk like honey.
Wait until the cookies are completely cool before glazing them. Drizzle with a fork or piping bag, or dip the side of each cookie into the glaze. Let it set for a few minutes, and then serve