Preheat oven to 325 degrees F. Grease an 8-inch square pan and line with parchment paper.
Place the butter, unsweetened chocolate, white chocolate and cocoa powder in a medium heatproof bowl set over a saucepan of barely simmering water. Stir occasionally until completely melted and smooth.
Transfer melted chocolate mixture to a large bowl. Whisk in the sugar until completely combined. Add the eggs and vanilla extract and whisk until the mixture is thick and glossy. Using a rubber spatula, gently stir in the flour and salt, then fold in the chopped walnuts.
Scrape the batter into the prepared pan and smooth the top into an even layer. Bake until the brownies are slightly puffed and the outer edge looks set (an instant-read thermometer should read 190 degrees F), about 30 to 40 minutes.
Remove the pan from the oven and place on a wire rack to cool to room temperature. Refrigerate for at least 1 hour before serving. The brownies should be stored in an airtight container at room temperature for up to 3 days, or in the refrigerator for up to 2 weeks.