1.Preheat oven to 180°C/350°F. Grease three large oven trays; line with baking paper.
2.Combine butter and chocolate in a medium heatproof bowl over a medium saucepan of simmering water (do not allow water to touch bowl). Stir until melted; set aside.
3.Beat eggs, sugar and vanilla in a small bowl with an electric mixer for 10 minutes or until thick and creamy. Fold in sifted flour, then chocolate mixture; stand for 10 minutes.
4.Spoon mixture into a large resealable plastic bag or disposable piping bag fitted with a 1cm (½-inch) plain tube. Pipe 4cm (1½-inch) rounds, about 5cm (2 inches) apart, onto prepared trays. Bake for 8 minutes or until puffed and beginning to crack. Cool on trays.
5.Meanwhile, to make chocolate frosting; combine chocolate and butter in a medium heatproof bowl over a medium saucepan of simmering water. Stir until smooth. Whisk in sifted icing sugar; cool to room temperature. Beat with a wooden spoon until thick and spreadable.
6.Match up cookies into pairs that are the most similar in shape and size (there will be slight variations). Pipe chocolate frosting onto half the cookies, then sandwich together with remaining cookies.
Un-iced biscuits suitable to freeze. Chocolate and butter suitable to microwave.