Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper to prevent sticking.
In a medium mixing bowl, combine the old-fashioned rolled oats, quick-cooking oats, all-purpose flour, baking soda, salt, cinnamon, and freshly grated nutmeg. Whisk together until well combined.
In a separate large bowl, mix the melted unsalted butter and brown sugar until smooth. Add the egg yolk, milk, and vanilla extract. Stir until everything is well blended.
Gradually add the dry ingredient mixture into the wet ingredients, stirring until just combined. It’s important not to overmix here; you want the dough to be soft and slightly sticky.
Gently fold the freshly grated zucchini and chocolate chips into the dough until evenly distributed.
Using a tablespoon or a cookie scoop, drop rounded balls of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden, and the centers look set but slightly underbaked. They will continue to firm up as they cool.
Allow the cookies to cool on the baking sheet for about 5 minutes before transferring them to a wire rack to cool completely. Enjoy your freshly baked Chewy Oatmeal Zucchini Cookies with a cup of tea or coffee!