Grease a pudding dish or a shallow baking dish with the capacity of about 1 1/2-quarts with some of the butter.
Put the raisins in a small bowl, pour the rum over and microwave them for 1 minute, then leave them to stand. This is a good way to soak them quickly but juicily.
Make the sandwiches with the brown bread, butter and ginger jam (2 tablespoonfuls in each sandwich); you should have some butter left over to smear the top later. Now cut the sandwiches in 1/2 into triangles and arrange them evenly along the middle of the dish. I put 1 in the dish with the point-side uppermost and so on, then squeeze a sandwich-triangle down each side - but you do as you please. Sprinkle with the raisins and unabsorbed rum that remains in the bowl.
Whisk the egg yolks and egg together with the sugar, and mix in the cream and milk. Pour this over the triangles of bread and leave them to soak up the liquid for about 10 minutes, by which time the pudding is ready to go into the oven. Smear the bread crusts that are poking out of the custard with the soft butter, mix the ground ginger and Demerara sugar together and sprinkle this mixture on your buttered crusts and the lightly over the rest of the pudding.
Sit the pudding dish on a baking sheet and put in the oven to cook for about 45 minutes or until the custard has set and puffed up slightly. Remove, let sit for 10 minutes - by which time the puffiness will have deflated somewhat - and spoon out into bowls, putting a pitcher of custard, should you wish, on the table to be served alongside.