Make the cranberries: In a small bowl, combine the cranberries and Bourbon. Soak for at least 1 hour, then drain the cranberries through a fine-mesh sieve, reserving the Cranberries infused Bourbon for another use.

While the cranberries soak, make the pumpkin custard: In a medium saucepan set over medium heat, stir together the milk, condensed milk, evaporated milk, brown sugar, allspice, cloves, cinnamon sticks, aniseeds and salt. Bring to a simmer, stir in the pumpkin purée, reduce the heat to medium-low and simmer until the mixture thickens and coats the back of a spoon, 8 to 10 minutes. Set a fine-mesh sieve over a medium bowl and force the mixture through the sieve, using the back of a spoon or a rubber spatula to push the mixture through. Add the butter and vanilla to the warm, strained pumpkin mixture and stir until the butter melts. Add the egg yolks and stir gently until combined. Add the bread cubes and set the mixture aside until the bread is softened and has absorbed the custard, about 20 minutes. Stir in the reserved Cranberries.

Make the caramel: While the bread is soaking, heat a small saucepan over medium-high heat. Add the sugar and water and bring to a boil. Cook, carefully swirling the pan every few minutes, until the liquid turns a light caramel color, about 8 minutes. Pour the caramel into a 9-by-13-inch baking dish, tipping and tilting the pan to coat it. Set the pan aside.

Preheat the oven to 350°. Add the reserved bread mixture to the caramel-coated baking dish. Place the pan in a larger baking dish (or roasting pan) and pour in just enough hot water to come halfway up the sides of the outer pan. Place the pans in the oven and bake until the custard is just set and jiggles slightly in the center, about 50 minutes. Remove the bread pudding from the water bath, wipe off the excess water with a kitchen towel and invert the hot bread pudding onto a serving platter. Use a sharp knife to cut the bread pudding into squares and serve the bread pudding warm or at room temperature with the crème fraîche.