Put the sugar, syrup and butter in a saucepan. Bring to a simmer, then bubble for 1-2 mins, stirring. Set aside to cool for 10 mins.
Tip the flour, bicarb and spices into a large bowl. Add the syrup mixture and the egg, stir to bring everything together, then gently knead in the bowl until smooth. The dough will feel a little soft, but will firm up once cooled. Wrap and chill for at least 30 mins.
Remove the dough from the fridge and leave at room temperature until softened. Heat oven to 200C/180C fan/gas 6 and line two baking trays with baking parchment.
Working with half the dough at a time (keeping the remaining dough well wrapped), roll out to the thickness of a £1 coin. Cut out 10-12 stars in descending size, re-rolling the offcuts if you need to. Arrange over the trays and bake for 8 mins until a few shades darker and puffed up a little. Cool on the trays for 5 mins, then transfer to a wire rack to cool completely. Will keep, un-iced, in an airtight container for up to two weeks.
Mix the icing sugar with enough water to make a thick, pipeable icing. Transfer to a piping bag and decorate. Pipe a blob of icing in the middle of each biscuit and stack them to make a tree, sticking the smallest star on top, standing upright.