Bread Pudding:

1. Preheat oven to 325 degrees. Lightly butter a 2-quart baking dish.
2. Cut the brioche into 1-inch pieces. Lay them on cookie sheet in an even layer and lightly toast them in the oven to dry about 10 minutes.
3. In a medium saucepan over medium heat, combine the milk, heavy cream, vanilla bean pod and seeds, and cinnamon sticks, heat until the cream is steaming and tiny bubbles have formed along the edges. Remove from the heat and cover with foil. Let steep for at least 20 minutes.
4. In a large bowl, whisk together the eggs, egg yolks, sugar, salt and pumpkin purée until smooth. Reheat the cream mixture until hot but not boiling. Temper the cream mixture into the egg mixture by pouring it little by little and whisking the whole time.
5. Place the toasted brioche in the prepared dish. Strain the custard over the bread and press down lightly with your hands so that all the bread is soaking. Let soak for 25-30 minutes.
6. Combine the sugar and cinnamon and sprinkle on top of the bread pudding.
7. Place the baking dish inside a roasting pan large enough to hold it. Fill the roasting pan with hot water until it reaches halfway up the sides of the baking dish. Bake for 1 hour 15 minutes or until set. Remove to a wire rack to cool.

Caramel Sauce:

1. Melt the butter in a saucepan over medium heat, add the brown sugar and cook for one minute, stirring constantly. Add the cream and salt, stir and bring to a boil, cook for 2 minutes. Remove from heat and stir in the vanilla.