Preheat the oven to 160 C. Line an 8.5x6.5 inch baking dish (see notes) with non-stick baking paper, leaving a little overhang for easy removal. Set aside.
In a microwave-safe mixing bowl, melt the butter, making sure it doesn't start boiling. Stir to melt any remaining lumps, instead of over-heating it. Alternately, melt the butter in a saucepan on the stove, then transfer to a mixing bowl.
Now stir in the sugar, whisking very well to combine. Then add the eggs and vanilla, whisking vigorously for about 2 minutes by hand or with a hand mixer, until the mixture thickens a little and looks paler in colour. While this isn't strictly necessary, I use this method in all brownie recipes to create a nice crackly crust so I recommend it!
Now sift in the flour, cocoa and salt, if using. Fold gently to combine, taking care not to over mix the batter. It will be fairly thick.
Spoon the batter into the prepared baking dish, spreading it out evenly. Sprinkle chopped walnuts over the top.
Bake for 25 to 30 minutes, until a toothpick poked in the center comes out with a few moist crumbs. The top will still seem quite soft and the sides will appear more cracked than the center in my experience. Avoid over-baking the brownies because they will continue to cook as they cool and if baked too long, they will be dry instead of deliciously gooey.
Let cool in the dish for 15 minutes, then lift the brownies out using the paper and leave them on a wire rack to cool completely. They will firm up as they cool and the top will get a nice crackly look as you cut the brownies. Slice into 10 equal pieces and dig in!
On day one these brownies are gooey and buttery and they taste even better on day two when they become more chewy. Store in an airtight tin for 3 to 4 days at at room temperature, about 10 days in the fridge (bring to room temperature before eating) and longer in the freezer, if you have any leftovers! Happy baking :)