Preheat oven to 175°C / 350°F (160°C fan). Line an 8×8 inch baking pan with parchment paper, leaving an overhang on two sides.
Melt the butter in a saucepan over low heat or in a microwave-safe bowl. Whisk in the sugar until combined. Cool for 5 minutes.
Add the eggs one at a time, whisking vigorously by hand for 30 seconds after each. Add the vanilla extract.
Sift in the cocoa powder, then add the flour, salt, and baking powder. Fold with a spatula until just combined — stop the moment you no longer see dry streaks.
Fold in the 10 roughly chopped Oreos. Pour into the prepared pan and spread level.
Press the 6 whole or halved Oreos onto the surface of the batter, partially embedding them.
Bake on the centre rack for 25 to 28 minutes. Start checking at 23 minutes — a toothpick inserted between Oreos should come out with a few moist crumbs, not wet batter and not clean.
Cool completely in the pan on a wire rack — at least 1 hour. Refrigerate for 30 minutes for cleaner slices. Lift out using the parchment overhang and cut into 16 squares.