Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
Place the shredded zucchini in a clean kitchen towel and squeeze out excess moisture. Set aside.
In a medium bowl, whisk together the rolled oats, all-purpose flour, baking soda, baking powder, salt, ground cinnamon, and ground nutmeg.
In a large bowl, using an electric mixer, cream the softened butter, granulated sugar, and light brown sugar together until light and fluffy, about 2-3 minutes.
Add the egg and vanilla extract to the butter mixture and beat until fully combined.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined.
Fold in the shredded zucchini and semi-sweet chocolate chips until evenly distributed.
Drop rounded tablespoons of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake in the preheated oven for 10-12 minutes, or until the edges are golden brown and the centers are set.
Remove the cookies from the oven and allow them to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.