To make the pudding: Generously butter a ovenproof baking dish. Spread each slice of barmbrack with butter.
Cover the bottom of the dish with a layer of barmbrack, buttered side up. Sprinkle with some of the nutmeg. Repeat layering until the barmbrack and nutmeg are used up.
In a medium saucepan over medium heat, heat the cream and milk. Add the eggs, stir in the sugar and rum, and pour over the layers of barmbrack making sure each part is covered. Cover with plastic wrap and refrigerate for at least 4 hours or overnight.
Preheat the oven to 300 degrees F. Put the baking dish in a roasting pan and fill with water to come two-thirds of the way up the sides. Bake for 40 to 45 minutes, until the pudding is firm and browned on top. Serve with warm Custard Sauce.
To make the custard: In a medium saucepan over medium heat, heat the milk. Whisk egg yolks and sugar together in a large metal bowl. Gradually whisk hot milk into yolk mixture, then return mixture to saucepan. Stir gently over medium heat for 6 to 8 minutes, until custard starts to thicken and coats the back of a spoon (do not allow to boil). Transfer to a medium bowl, stir in the vanilla and Irish whiskey, and let cool. Cover and refrigerate until cold, about 3 hours. (Can be refrigerated for up to 24 hours.)