Start by preheating your oven to 350°F (175°C). This ensures that your cookies bake evenly and come out perfectly chewy.
Line a baking sheet with parchment paper. This will help prevent your cookies from sticking and make for an easier cleanup.
In a large mixing bowl, combine the old-fashioned rolled oats, quick-cooking oats, all-purpose flour, baking soda, salt, cinnamon, and freshly grated nutmeg. Mix well to ensure that all the dry ingredients are evenly distributed.
In another bowl, whisk together the melted unsalted butter and brown sugar until smooth. Add in the egg yolk, milk, and vanilla extract, then mix until well combined.
Using a grater, grate your zucchini into fine pieces. You can choose to squeeze out some excess moisture if desired, but the moisture from the zucchini will help keep your cookies soft.
Add the wet mixture to the dry ingredients and stir until just combined. Gently fold in the grated zucchini and chocolate chips, being careful not to overmix the dough.
Using a cookie scoop or spoon, drop tablespoon-sized portions of the dough onto your prepared baking sheet, spacing them about 2 inches apart to allow for spreading.
Place the baking sheet in the preheated oven and bake for 10-12 minutes, or until the edges are lightly golden. The centers may look slightly underbaked, but they will firm up as they cool.
Once baked, remove the cookies from the oven and let them cool on the baking sheet for about 5 minutes before transferring them to a wire rack to cool completely. Enjoy your chewy oatmeal zucchini cookies warm or at room temperature!