Step 1: Preheat your oven to 180°C (350°F) and line a 9x13 inch baking pan with parchment paper, leaving an overhang on the sides for easy removal.
Step 2: In a medium bowl, whisk together the flour, cocoa powder, baking powder, and salt. Set aside.
Step 3: For the brownie layer: In a heatproof bowl, melt 150g of the chopped dark chocolate and the butter together either over a double boiler or in the microwave in 30-second intervals, stirring until smooth. Let cool slightly.
Step 4: Whisk in one room temperature egg and the granulated sugar into the cooled chocolate mixture until combined. Stir in ½ teaspoon of vanilla extract.
Step 5: Gradually add half of the dry ingredients to the wet ingredients for the brownie, mixing until just combined. Spread this brownie batter evenly into the prepared baking pan.
Step 6: For the cookie layer: In a separate bowl, cream together the remaining 75g of chopped dark chocolate, the Demerara or raw sugar, and the remaining 56g butter until light and fluffy.
Step 7: Beat in the second room temperature egg and the remaining ½ teaspoon of vanilla extract until well combined.
Step 8: Gradually add the remaining half of the dry ingredients to the cookie mixture, mixing until just combined. Fold in the chocolate chips.
Step 9: Carefully dollop spoonfuls of the cookie dough over the brownie layer, then gently spread it out evenly to cover the entire surface. This can be tricky; try to avoid disturbing the brownie layer too much.
Step 10: Bake for 30-35 minutes, or until the edges are set and a toothpick inserted into the cookie layer comes out with moist crumbs, not wet batter. The center might look slightly soft.
Step 11: Let the brookies cool completely in the pan on a wire rack before lifting them out using the parchment paper overhang. Slice into squares and serve.