To make the ginger syrup, combine 200ml water, 100g dark brown sugar, 1 cinnamon stick, 1 peeled and thinly sliced thumb-sized piece of ginger and ½ tsp vanilla extract in a saucepan. Bring to the boil, then reduce the heat and simmer for two minutes. Allow the syrup to cool, then strain out the spices and store in the refrigerator. On a saucer, combine 4 tbsp brown sugar with 1 tsp cinnamon and 1 tsp ground ginger.
Dip the rim of a martini glass in a little water and then into the sugar mixture. Half-fill a cocktail shaker with ice. Add 30ml vodka, 30ml Irish cream liqueur, 30ml single cream, 30ml of the ginger syrup and 30ml cold espresso. Shake heartily, then strain into the prepared martini glass. To serve, top with softly whipped cream and sprinkle with gingerbread crumbs.