Preheat your oven to 350 degrees F. Line two baking sheets with parchment paper and set them aside.

Grate the zucchini on the large holes of a box grater. Pile it onto a clean kitchen towel or several layers of paper towels, then squeeze firmly until you have removed as much water as you can. You want the zucchini to feel almost dry to the touch. This step keeps the cookies from spreading too flat or turning gummy.

In a medium bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, and salt. Set aside.

In a large bowl, whisk together the melted butter, maple syrup, and brown sugar until combined and slightly thickened, about 1 minute. Add the egg and vanilla and whisk again until smooth.

Add the squeezed zucchini to the wet ingredients and stir to combine. Pour in the dry ingredients and fold with a rubber spatula just until no streaks of flour remain. Do not overmix.

Scoop rounded tablespoons of dough onto the prepared baking sheets, spacing them about 2 inches apart. The dough will be soft but should hold its shape reasonably well.

Bake one sheet at a time on the center rack for 12 to 14 minutes, until the bottoms are lightly golden and the tops look just set. The centers may still look very slightly underdone when you pull them from the oven, which is exactly right.

Let the cookies sit on the hot pan for 3 minutes, then transfer them to a wire rack to cool completely. Once cooled, dust lightly with powdered sugar using a fine mesh strainer or small sifter before serving.