Preheat oven to 350°F/180°C. Line a 9x9-inch (or 8x8-inch) baking pan with tin foil, leaving enough overhang on the sides for lifting the brownies out after baking.
To make the cookie dough: In a medium bowl sift together flour, baking soda and salt. Set aside.
In a mixer bowl fitted with the paddle attachment, beat butter, brown sugar, and granulated sugar on medium speed until light and fluffy, 3-4 minutes. Beat in egg and vanilla. Add flour mixture and mix just until combined. Do not overmix. Fold in chocolate chips.
Layer the cookie dough on the bottom of prepared pan, pressing down to form an even layer. Bake for 8 minutes until just beginning to set. Allow to cool slightly on a wire rack. Meanwhile, prepare the brownie batter.
To make the brownies: In a large heatproof bowl, place chocolate and butter. Heat in the microwave in 20-second intervals, stirring in between each interval, until melted (or set it over a saucepan of simmering water, stirring occasionally). Add cocoa powder and sugar and whisk until combined. Stir in eggs. Add flour and salt and fold, using a rubber spatula, just until combined. Set aside.
Pour brownie batter slowly over the Oreos and smooth the top. Bake until a toothpick inserted into the center of the brownies come out with moist crumbs, 20-25 minutes. Let brownies cool completely on a wire rack, then refrigerate until set for easy cutting, at least 4 hours. Lift brownies out of the pan using tin foil and cut with a sharp knife into 16 squares. Store brownies at room temperature or in the fridge in an airtight container for up to 3 days.