Preheat your oven to 350 degrees F. Line two baking sheets with parchment paper.

Grate the zucchini on the fine side of a box grater. Transfer it to a clean kitchen towel and squeeze out as much moisture as you can. The drier the zucchini, the better your cookies will hold their shape. Set it aside.

In a medium bowl, whisk together the flour, baking soda, baking powder, salt, and cardamom. If you have never baked with cardamom before, start with just 1/4 teaspoon and taste the dough before adding more. It is a bold spice that can sneak up on you.

In a large bowl, beat the softened butter and granulated sugar together with a hand mixer on medium speed until the mixture is slightly fluffy, about 2 minutes. Add the egg, vanilla, and orange zest and mix until combined. The batter should smell wonderful at this point.

Fold the squeezed zucchini into the butter mixture with a rubber spatula until evenly distributed.

Add the flour mixture and stir gently until a soft dough comes together. Stop mixing as soon as you no longer see dry flour. Overmixing will make the cookies tough.

Scoop rounded tablespoons of dough onto the prepared baking sheets, spacing them about 2 inches apart. Press each one down lightly with your fingers. These cookies do not spread much, so a gentle flatten helps them bake evenly.

Bake for 11 to 13 minutes, until the edges are just set and the tops look dry. The centers will still look slightly underdone, and that is fine. They finish cooking on the hot pan. Let the cookies cool on the baking sheet for 5 minutes, then move them to a wire rack to cool completely.

While the cookies cool, make the orange glaze. In a small bowl, stir together the sifted powdered sugar, orange juice, and orange zest if using. The glaze should be thick enough to coat a spoon but still drizzle easily. If it is too thick, add orange juice a teaspoon at a time. If it is too thin, add a little more powdered sugar.

Once the cookies are completely cool, drizzle or spread a thin layer of orange glaze over each one. Let the glaze set for about 10 to 15 minutes before stacking or storing.