1.Chop butter; place in medium saucepan with sugar and golden syrup. Stir over low heat until smooth; transfer to large heatproof bowl. Cool for 15 minutes.
2.Stir extract, egg, cream and sifted soda, then sifted flour into butter mixture. Turn dough onto floured surface; knead until smooth. Divide dough in half. Enclose in plastic wrap; refrigerate 1 hour.
3.Preheat oven to 180°C/350°F.
4.Roll half the dough between sheets of baking paper until 3mm (⅛ inch) thick. Cut dough into tree shapes, using template as a guide; re-roll dough scraps as necessary. Transfer trees to baking-paper-lined oven trays. Refrigerate 20 minutes.
5.Bake trees about 10 minutes. While trees are hot, use a pizza cutter or sharp knife to cut out puzzle shapes. Cool on trays. Repeat with remaining dough.
6.To make royal icing, beat egg white in small bowl with electric mixer until white is just broken up. Gradually beat in sifted icing sugar until firm peaks form; stir in enough juice to make icing a piping consistency. Keep surface of icing covered with plastic wrap to prevent it drying out.
7.Fit a small piping bag with a small plain piping tube; half-fill with royal icing, use to pipe around edge of each puzzle piece in an unbroken line.
8.Tint remaining icing blue. Fit a small piping bag with a star tube, half-fill with icing, use to pipe stars on each puzzle piece. Top each star with a silver cachous before icing sets. Stand trees about 2 hours or until icing sets.
We used a light dusting of edible silver dust (available at cake decorating shops) to make the trees look more festive. Biscuits will keep in an airtight container for up to one week. Decorate up to 2 days ahead.