Preheat the oven to 350°F (175°C). Line a square 9x9-inch (23 cm) baking pan with parchment paper, ensuring the edges extend beyond the pan for easy lifting after baking.
In a medium mixing bowl, combine the melted butter, granulated sugar, eggs, and vanilla extract. Whisk vigorously until the mixture becomes glossy and smooth. Add in cocoa powder, flour, baking powder, and salt, stirring gently until the dry ingredients are fully incorporated. Transfer the batter into the prepared pan, spreading it in an even layer.
In a separate bowl, stir together the creamy peanut butter and powdered sugar until the mixture becomes smooth and uniform. Spoon dollops over the brownie layer, then use a spatula to lightly spread the filling across the surface.
To prepare the cookie topping, beat the softened butter together with brown sugar and white sugar in a new bowl until light and fluffy. Mix in the egg and vanilla until combined. Fold in the flour, baking soda, and salt until a dough forms. Stir in the chocolate chips.
Drop spoonfuls of cookie dough over the peanut butter layer. Gently spread it across the top using your hands or a spatula—it doesn’t need to be perfectly smooth, as it will spread during baking.
Place the pan in the preheated oven and bake for 30 to 35 minutes, or until the surface turns golden brown and a toothpick inserted into the center emerges with a few moist crumbs.
Let the brookies rest in the pan for at least 30 minutes before lifting out using the parchment handles. Cut into squares and serve.