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Soak sultanas and currants in the rum for 1 hour.
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Preheat oven to 180C degrees.
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Fill a roasting pan with enough hot water to come halfway up the side of the 1 quart baking dish you plan to use for the pudding.
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Place it in the oven.
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Butter the baking dish.
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Butter the bread.
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Cut into triangles and arrange in the dish, alternately with the fruit, until all are used.
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In a bowl, whisk together the eggs and sugar until pale.
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Heat the milk to boiling point and whisk into the egg mixture.
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Add any remaining rum and the vanilla.
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Pour over the bread and let stand for 10 minutes to allow it to soak up the egg custard.
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Place the dish in the roasting pan in the oven and cook for 40-45 minutes, or until the custard is just set.
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If the top browns too quickly, place tin foil over it to prevent burning.
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Serve warm with ice cream or cream.