Puding De Castañas (Portuguese Chestnut Pudding)

Heat 1/2 cup sugar and the rum in a heavy skillet or saucepan, stirring constantly until it melts and turns a dark golden color. Pour immediately into a metal ring mold and tilt to cover entire bottom with liquid caramel.
Preheat oven to 325 degrees.
Place the cream in a saucepan over medium heat and stir while heating, but do not let it come to a boil. Set aside.
In a large bowl, beat the eggs, yolks and sugar until smooth and light yellow in color. Add vanilla and mix well.
Add the chestnut puree and mix well. Pour the hot cream into the chestnut mixture and stir until smooth and all ingredients are incorporated evenly.
Fit a dish towel in the bottom of a high-sided pan that will accomodate the ring mold. Place the metal ring mold in the pan, then place both on the oven rack.
Pour the pudding mixture into the ring mold, then carefully pour the boiling water into the larger pan to a level that reaches halfway up the side of the ring mold.
Bake pudding until set, about 1 hour or until a knife comes out reasonably clean. Cool flan on a metal rack, then refrigerate for at least 3 hours, but preferably overnight.
To unmold, run a rubber spatula around edge of mold, all the way down to the bottom and all the way around.
Place the serving platter over the mold, then quickly flip over so that the flan slips onto the serving plate.
Scoop any leftover caramel onto the flan and serve.
Note: you can also make these individually in small ramekins.