Thoroughly combine the milk, oil and egg in a bowl. Mix in the flour and all the remaining ingredients, transfer to the prepared tin.
Bake for approx. 25 mins. in the centre of an oven preheated to 180°C. Remove from the oven, allow to cool a little, then leave to cool completely on a rack, cut into squares.
Mix the water, Kirsch and icing sugar, drizzle over the gingerbread.
Mix the chestnut puree and cream until smooth, transfer to a piping bag with a serrated nozzle (approx. 10 mm diameter). Pipe the vermicelli onto the gingerbread squares.