Preheat the oven to 350˚F (180˚C). Line your (8x8 inch/20x20 centimeter) pan with parchment paper.
Place the chocolate in a heatproof mixing bowl.
Separately, in a small metal saucepan (so you can see it change color), melt the butter over low heat.
Once melted turn the heat up to medium and allow the butter to simmer gently until it turns golden and smells nutty, up to 10 minutes. At this point, keep an eye on it constantly and take it to a deep golden brown, removing it from the heat as soon as it's reached this level (as it will continue cooking beyond this moment).
Allow to cool for 5 minutes, then pour the browned butter (milk solids and all) straight over the chocolate. Leave to sit for 2 minutes before stirring until the chocolate is completely (or mostly) melted.
In a large bowl, use an electric mixer to mix the eggs and both sugars just until evenly combined.
Gently fold in the melted chocolate and butter, then sift in the flour and cocoa powder, and add the salt.
Fold the flour gently into the mix, stopping as soon as everything is combined- you should be left with a glossy batter.
Pour the brownie mix into the prepared pan. Sprinkle with some flaky sea salt, then bake for around 35-40 minutes until the top is glossy and an inserted skewer comes out with damp crumbs (you want to err on the side of undercooked with brownies).
Eat warm or leave the brownies to cool in their tin (they will cut more neatly if allowed to fully cool and set). They're at their best the next day.