Preheat the oven to 350°F (175°C). Grease a 9×9 inch baking pan and line it with parchment paper, leaving an overhang for easy removal.
Prepare the brownie layer: In a large bowl, combine melted butter and 1 1/2 cups granulated sugar. Whisk until smooth.
Add 3 eggs and 2 teaspoons vanilla extract to the butter and sugar mixture. Whisk until fully combined.
In a separate bowl, sift together 1 cup flour, cocoa powder, salt, and baking powder.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Fold in the white chocolate chips.
Spread the brownie batter evenly into the prepared baking pan.
Prepare the sugar cookie layer: In a medium bowl, cream together 1/4 cup softened butter and 1/2 cup granulated sugar until light and fluffy.
Beat in 1 egg and 1 teaspoon vanilla extract until combined.
In a separate bowl, whisk together 1 1/4 cups flour, 1/4 teaspoon baking powder, and 1/8 teaspoon salt.
Gradually add the dry ingredients to the wet ingredients, mixing until a soft dough forms.
Drop spoonfuls of the sugar cookie dough evenly over the brownie batter. Gently spread or pat the cookie dough to cover the brownie layer as much as possible without mixing the two batters.
Bake in the preheated oven for 28 to 32 minutes, or until the sugar cookie layer is set and a toothpick inserted into the center comes out with moist crumbs but no raw batter.
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 sugar cookie brownies out of the pan. Cut into 16 squares and serve.