Preheat the oven to 180 degrees C. Grease and flour two 20cm round cake tins.
Sift together the flour, cocoa powder, baking powder and salt; set aside. Melt the chocolate in a cup or small bowl in the microwave. Stir every 15 seconds until smooth.
In a large bowl, beat the butter and sugar with an electric mixer until light and fluffy. Mix in the mashed potatoes and then the eggs, one at a time. Stir in the melted chocolate. Stir in the dry ingredients alternating with the milk just until everything is mixed. Divide evenly between the prepared pans and smooth the surface if needed.
Bake in the preheated oven until a knife inserted into the centre of the cake comes out clean, 25 to 30 minutes. Cool in the pans set over a wire rack.