Beat the egg yolks with 2 tablespoons of icing sugar and butter, which are left to soften at room temperature. Beat until you have a smooth cream. Boil the milk with cocoa and the remaining powdered sugar.
In a wide, shallow bowl, use a fine grater to grate the chocolate. Cut each biscotti into 4 pieces and glue them two by two with the prepared cream. Then dip them in cold milk syrup and roll them in grated chocolate.
Keep the cakes cold before serving them, so as not to melt the chocolate.