Brown the Butter: Cube the unsalted butter and melt it in a light-colored skillet over medium heat for 5 to 8 minutes until golden brown with a nutty aroma. Allow to cool slightly.

Mix Wet Ingredients: Combine the cooled brown butter with dark brown sugar and granulated sugar in a large bowl. Blend until smooth, then add in the egg and blend until fully integrated.

Combine Dry Ingredients: In a separate bowl, whisk together all-purpose flour, baking soda, and fine sea salt. Gradually incorporate into wet ingredients until just combined.

Fold in Add-ins: Gently fold in chopped dark chocolate and Oreos until evenly dispersed. Be careful not to overmix.

Chill Dough: Cover with plastic wrap and refrigerate for 30 to 60 minutes. Preheat oven to 350°F (180°C) while chilling.

Bake Cookies: Scoop the chilled dough onto a lined baking sheet and bake for 10 to 12 minutes, looking for lightly browned edges while centers remain soft.

Cool: Let cookies rest on the baking sheet for about 5 minutes before transferring to a wire rack to cool completely.