Line a 8x8 square pan with parchment paper, coming up to the sides, for easy removal once baked. Grease with butter, keep aside.
Preheat oven at 180 Celsius.
In a heavy bottomed pan, melt butter on a low heat. Once nearly melted, remove from flame. It will melt fully in the residual heat. Add the finely chopped chocolate to this and stir till the chocolate fully melts in the heat of the melted butter. Keep aside.
In a large bowl, whisk the 4 eggs with a balloon whisk or electric whisk until nearly tripled in volume.
Add half the sugar along the sides so as not to knock out the air from the eggs. Whisk gently until incorporated. Repeat the same with remaining sugar until the sugar no longer feels grainy to touch in the egg mixture.
Add the chocolate-butter mixture to this. Whisk gently to combine well.
Add 1/3rd of the quartered Oreos to the batter.
In a small bowl, mix with a fork- the flour, cocoa and salt and add this to the above mixture. Whisk well to combine everything together.
Pour this into the greased parchment.
Top this with the remaining Oreos arranged in a single layer all over.
Bake in the middle of a 180 C oven for 40 minutes, until a tester poked into the center comes out nearly clean.
Remove from oven and rest for 10 minutes. Pull out with the parchment intact and cool on a wire rack for 2-3 hours or overnight. Cut into 2" squares (16 pieces) and peel off parchment. Refrigerate for a few hours for a great texture.