Melt the chocolate and butter in a large bowl set over a saucepan of gently simmering water. Whisk the sugar and eggs with an electric whisk until very thick and the whisk leaves a trail when lifted out of the mixture. Fold in the melted chocolate then the flour and baking powder.
Pour the mixture into a 20 cm (8 inch) square cake tin lined with non-stick baking paper and sprinkle with the pistachios. Bake in a preheated oven, 180°C (350°F), Gas Mark 4, for about 25 minutes until the top is crusty but the centre is still slightly soft. Allow to cool and harden in the tin.
To make the sauce, heat the chocolate, milk and sugar gently in a saucepan, stirring until smooth. Allow to cool, cover and chill until required.
When ready to serve, lift the brownies out of the tin using the paper. Cut into small squares, lift off the paper and transfer to serving plates. Add scoops of vanilla ice cream and serve with the reheated chocolate sauce.