For the dough, whisk butter and brown sugar with the whisks of the mixer until foamy. First stir in syrup, then egg. Mix flour, baking powder, cocoa, 3 tsp. gingerbread spice and 1⁄4 tsp. salt.
Stir the mixture into the butter-sugar mixture. Shape into a ball, cover and chill for at least 2 hours.
Preheat the oven (electric cooker: 175 °C/circulating air: 150 °C/gas: see manufacturer). Line two baking trays with baking paper. Form the dough into walnut-sized balls. Spread on the baking trays. Bake one after the other in a hot oven for about 12 minutes.
Take it out of the oven. Leave to cool on the tray for about 10 minutes. Let it cool down on a cake rack.
For the icing sugar, 1⁄4 tsp. gingerbread spice and approx. 3 tbsp. water stir until smooth. Spread on the cookies and let dry.