Preheat the oven to 350°F or 180°C.
Line a 9" x 13" or 33 x 22 cm baking pan with parchment paper and set aside.
Melt the semisweet chocolate, unsweetened chocolate and butter together. Stir until smooth.
Whisk together the flour, cocoa, baking powder and salt. Set aside.
Place the eggs and sugar into a large mixing bowl. Mix until blended.
Add half of the dry ingredients followed by the melted chocolate/butter and vanilla.
Blend in the remaining dry ingredients.
Transfer a third of the batter to the parchment-lined baking pan and use an offset metal spatula to spread it in the pan.
Evenly place the Kit Kat bars over the batter. There will be six bars going down and four bars going across.
Cover the Kit Kat bars with a third of the batter, using the offset spatula to guide the batter.
Place the Oreo cookies on the batter. Spoon the remaining batter over the cookies and use the offset spatula to gently spread the batter over them.
Bake in your preheated oven for 35 minutes. Remove from the oven and cool completely before cutting into bars.