Preheat the oven to 350 degrees. Prepare a 15x21 rimmed baking pan (three-quarter sheet pan) with parchment paper.
Mix the brownies according to the instructions on the box. Spread the batter in an even layer on the prepared baking pan.
Bake the brownies until done, about 20 to 25 minutes. Place the baking sheet on a wire rack and let the brownies cool completely.
In a mixing bowl, beat the cream cheese and butter until mixed and creamy. Add the vanilla, scraping down the sides and blending well.
To the cream cheese, add the powdered sugar and beat on low until it is incorporated. Then, increase the speed and blend the cream cheese until the powdered sugar is completely incorporated and smooth.
Cut the brownie into 4 equal rectangles.
Place one of the brownie rectangles on a serving platter. Spread the brownie with ¼ of the cream cheese mixture. Repeat the layers, stacking the brownies and cream cheese, until all of the brownies are used.
Over the final layer of cream cheese, drizzle with the chocolate syrup and top with chocolate curls.
Refrigerate overnight before serving.