Preheat oven to 180°C/ 350°F/ Gas Mark 4. Grease an eight-inch square cake tin. Sift flour and baking powder. Combine chocolate and butter in a large microwave bowl and soften, uncovered, for a minute on Microwave HIGH (100%) or melt it in a double boiler.
Beat in sugar and vanilla essence and blend well. Add the sifted flour, walnut kernels and milk and mix well. Pour the mixture into the prepared cake tin. Bake in the preheated oven for twenty five to thirty minutes.
Place on a wire rack to cool. Cut into squares and serve.