How to Make It
In a medium saucepan, combine the milk and cream. Add the cinnamon sticks, ginger, vanilla bean and cloves and cook over moderate heat until just steaming; do not let the milk boil. Remove the saucepan from the heat, cover and let stand until the milk is fragrant, about 30 minutes.
Preheat the oven to 375°. Lightly butter a 9-by-13-inch glass or ceramic baking dish. On a rimmed baking sheet, toast the cubed brioche in the oven for about 8 minutes, or until dry and golden. Spread the brioche cubes in an even layer in the prepared baking dish .
Rewarm the spiced milk over moderate heat until steaming, then strain it into a heatproof medium bowl.
Meanwhile, in another medium bowl, combine the eggs, egg yolks, pumpkin puree and salt and whisk until blended and smooth. Whisk in 1/2 cup of the sugar. Gradually whisk 1 cup of the hot milk into the pumpkin mixture, then whisk the mixture back into the remaining milk.
Pour the pumpkin custard evenly over the brioche and cover with plastic wrap. Let stand until the brioche has absorbed the custard, about 30 minutes. Discard the plastic wrap.
In a small bowl, combine the remaining 3 tablespoons of sugar with the cinnamon and sprinkle over the bread pudding. Set the baking dish in a large roasting pan and add enough hot water to the pan to reach halfway up the side of the baking dish.
Bake the bread pudding, uncovered, for about 45 minutes, until puffed and set. Let cool slightly, spoon into bowls and serve warm, with the Caramel Rum Raisin Sauce drizzled on top.