Preheat oven to 175°C and prep an 8 inch square pan by greasing and lining it with parchment paper. Leave an overhang of the parchment paper on two opposite sides so you can easily lift out the brownies in a “sling”
Create a double boiler to melt the chocolate and butter: heat about 2 inches of water in a saucepan. Once simmering, reduce the heat to medium low and add a heat-proof mixing bowl on top (placing it carefully so that the base is not touching the water). Add the chopped chocolate and butter, stirring regularly until melted and smooth. Remove the bowl from heat and give it a good stir to make sure that this mixture is evenly melted and completely smooth. Set aside to cool.
Beat the eggs (preferably using a hand or electric mixer) until they start to froth. Then, slowly add the sugar (over the span of 30 seconds to 1 minute or so) whilst continuing to beat the eggs with the mixer. Continue beating until this wet mixture has an almost creamy consistency. Mix in the vanilla.
Check the melted butter and chocolate mixture to make sure that it’s now lukewarm (not hot) before stirring it into the eggs and sugar mixture.
Now sift in the flour, cocoa powder and salt; and fold these dry ingredients into your wet mixture until just combined. You can do so using a rubber spatula, or stir it in at low speed using a hand-held mixer.
Gently fold in the chocolate chips and toasted walnuts too. Be careful not to overmix.
Pour the batter into the pan, smoothening out the surface with an offset spatula. Press a few more chocolate chips onto the top and pop the pan in the oven to bake for 18 – 20 minutes or so.