1. Preheat the oven to 325°F. Line an 8-by-8-inch glass baking dish with foil.
2. In a large microwave-safe bowl, melt the butter and chocolate for about 45 seconds on high power. Stir and continue heating in 20-second intervals, stirring after each interval, until the chocolate is melted and smooth.
3. Stir in the granulated sugar, brown sugar, and cocoa powder. If still very hot, let cool slightly before adding in the vanilla extract, eggs, and egg yolk. Stir until very well combined.
4. Add in the flour, cornstarch, and salt and stir until just combined, then fold in the walnuts. The batter will be thick.
5. Pour into the prepared pan and bake for 35 minutes, or until a toothpick inserted into the center comes out with just a few moist crumbs attached.
6. Let cool completely in the pan before cutting into squares and serving. The brownies can be stored in an airtight container at room temperature for 4 days, or in the fridge for 1 week.