For the cake: Preheat the oven to 375 degrees F and butter a 1 1/2-quart capacity baking dish.
Combine the sugar with the flour in a large bowl. Pour the milk into a measuring cup, beat in the egg, vanilla and melted butter and then pour this mixture over the sugar and flour, stirring with a wooden spoon to combine. Fold in the dates then scrape into the prepared baking dish. Don't worry if it doesn't look very full; it will by the time it cooks.
For the sauce: Sprinkle the sugar over the cake mixture and dot with butter. Pour over the boiling water (yes really!) and transfer to the oven. Set the time for 45 minutes, though you might find the dessert needs 5 or 10 minutes more. The top of the dessert should be springy and spongy when it's cooked; underneath, the butter, dark brown sugar and boiling water will have turned into a rich, sticky sauce. Serve with vanilla ice cream, creme fraiche or heavy or light cream, as you wish.