Preheat an oven to 350°F (180°C) and place an oven rack in the middle. Prepare the brownie pan by lining an 8x8 inch square pan or similar with parchment paper.
Mix the butter and the chocolate in a medium saucepan or a microwavable heatproof bowl. Heat it on low heat or in a double boiler, and stir with a wooden spoon or rubber spatula until it's all melted and combined. Alternatively, place a microwavable medium bowl in the microwave and melt it together in 20-second increments, stirring each time.
Once it's all melted, whisk in the granulated and soft brown sugar while it is still hot.
Beat in the eggs, one at a time, followed by the salt and vanilla.
Add the cocoa powder and flour into the chocolate mixture and whisk it well to combine it into a glossy chocolate batter.
Stir through the white and milk chocolate chunks or chips. Pour the batter into the prepared baking dish and use a spatula or knife to spread the batter to the sides of the pan.
Bake the brownies for around 28-32 minutes until a knife inserted into the pan comes out fairly clean with a few moist crumbs sticking to it. No wet batter should be left, but the brownie should still be moist. Take care not to overcook the brownies.
Leave the brownies in the pan to cool down completely on a wire rack before lifting them from the pan and slicing them.
Notes
US cup sizes are included, but note that these are smaller than metric cups. For best results, use grams