Preheat the oven to 170°C/ 150°C/325°F/Gas Mark3. Grease a 21cm x 21cm square cake tin and line with nonstick baking paper. Put the butter and dark chocolate in a heatproof bowl and place over a pan of barely simmering water (the base of the bowl should sit above the water without touching it).
Allow the butter and chocolate to melt together, stirring occasionally. When melted, remove the bowl from the heat and allow to cool for 5 minutes. Whisk in the sugar and vanilla until combined. Then, one at a time, whisk in the eggs.
Sift the flour, a pinch of salt and baking powder into the bowl and fold through until smooth; then add the white chocolate chips. Scrape the batter into the cake tin and bake for 35-40 minutes until a skewer inserted into the centre comes out with just a few crumbs on it. Cool in the tin for 5-10 minutes, then transfer to a wire rack to cool completely before slicing into 16 squares.