Preheat the oven to 180°C/356°F (without fan).
Use about 1 teaspoon of the butter to grease a dish measuring 16 x 21 cm/6 x 8 inches or similar.
Place the remaining butter into a small heatproof bowl over a pan of simmering water (a bain-marie) together with the chocolate. Ideally, the chocolate should be sitting on top of the butter so that it can melt more gently. If you have an induction stove, you can use a small saucepan directly on the stove.
Gently melt the butter and chocolate over very low heat.
As soon as the butter has melted, take the pan off the heat. Ideally, you do not want the mixture to become too warm.
Whisk until the chocolate has fully melted into the butter.
Add the vanilla to the melted chocolate.
Set the chocolate mixture aside to cool.
In a mixing bowl, whisk together the sugar and eggs until pale and light.
Add the chocolate mixture (which should now be at room temperature) and whisk to thoroughly combine.
Add the flour, salt and nuts.
Mix until the batter is just combined.
Pour the batter into the greased dish.
Use a spoon or spatula to ensure that the batter is even.
Bake for 20-25 minutes, or until the top of the brownies has evenly cooked. A skewer inserted in the middle of the brownies will likely come out with some batter attached. But if the batter looks still wet, cook the brownies for another 3-5 minutes. The brownies will continue to cook as they cool.
Leave the brownies to set for at least 30 minutes before slicing and serving.