Preheat the oven to 350°F (175°C). Grease a 9×13-inch baking pan and line it with parchment paper, leaving an overhang on the sides for easy removal.
Prepare the brownie layer: In a large bowl, whisk together the melted butter and 2 cups granulated sugar until combined.
Add the eggs one at a time, beating well after each addition, then stir in 1 teaspoon vanilla extract.
In a separate bowl, sift together 1 cup all-purpose flour, cocoa powder, baking powder, and 1/4 teaspoon salt.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined.
Pour the brownie batter into the prepared pan and spread evenly.
Prepare the sugar cookie layer: In a medium bowl, cream together the softened butter, 3/4 cup granulated sugar, and light brown sugar until light and fluffy.
Beat in the egg and 1 teaspoon vanilla extract until smooth.
In another bowl, whisk together 1 1/2 cups all-purpose flour, baking soda, and 1/4 teaspoon salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Drop spoonfuls of the sugar cookie dough evenly over the brownie batter in the pan. Use a spatula to gently spread and smooth the cookie dough to cover the brownie layer.
Bake in the preheated oven for 28 to 30 minutes, or until the cookie layer is set and a toothpick inserted into the center comes out with moist crumbs.
Remove from oven and allow to cool completely in the pan on a wire rack.
Once cooled, use the parchment paper overhang to lift the dessert out of the pan. Cut into 16 squares and serve.