Preheat oven to 350˚F (180˚C). Grease an 8x8 inch (20x20 cm) baking dish with butter or line with parchment.
In a small saucepan, melt butter over medium heat. Place the dark chocolate pieces in a heat-safe bowl. Once the butter has melted, remove from heat and pour over the chocolate. Whisk until the chocolate is melted and smooth. Set aside to cool slightly.
In a large bowl, beat together the sugar and eggs until light. Mix in vanilla extract. Slowly beat in the melted butter chocolate mixture until smooth.
In a medium bowl, whisk together the flour, cocoa powder, and salt. Gently fold into the wet ingredients until just combined. Transfer to prepared pan in an even layer.
Bake in the preheated oven until just set in center, 30-40 minutes. Allow to cool in pan to room temperature, about 1 hour.
Cut the cooled brownies into 9 even squares.
Melt the white chocolate in microwave in 20 second intervals, stirring in-between, until melted and smooth or in a double boiler. Transfer melted white chocolate to a piping bag or ziploc bag with corner snipped off.
Drizzle the white chocolate over the brownie squares. Allow to set before serving.