Start by placing the unsalted butter in a medium saucepan over medium heat. Allow it to melt, and then continue cooking it, stirring often. The butter will begin to foam, and eventually, you will notice a nutty aroma and brown flecks forming at the bottom. Once it turns a deep golden brown, remove it from the heat and let it cool slightly.
In a large bowl, whisk together the all-purpose flour, ground cinnamon, baking soda, salt, and ground nutmeg (if using). Set aside.
In another bowl, combine the dark brown sugar and granulated sugar. Pour in the browned butter (make sure it’s only slightly warm) and mix until combined. Add the large egg and vanilla extract, whisking until smooth.
Fold the shredded zucchini into the butter and sugar mixture. Be sure to squeeze out any excess liquid from the zucchini before adding it to avoid excess moisture in the cookies.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix; a few streaks of flour are okay.
Gently fold in the old-fashioned oats and semisweet chocolate chips, ensuring they are evenly distributed throughout the dough.
For best results, chill the cookie dough in the refrigerator for at least 30 minutes. This will help the cookies maintain their shape while baking.
Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
Using a cookie scoop or tablespoon, drop rounded balls of dough onto the prepared baking sheet, leaving space between each cookie. Sprinkle a pinch of flaky sea salt on top of each cookie.
Bake in the preheated oven for 10-12 minutes, or until the edges are golden and the centers look slightly underbaked. They will continue to firm up while cooling.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a cooling rack to cool completely. Enjoy your Brown Butter Zucchini Oatmeal Chocolate Chip Cookies with a glass of milk or your favorite beverage!