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Line a baking sheet with parchment paper. If necessary, roll out the puff pastry 1/4 inch thick. Using a biscuit cutter, stamp out six 4-inch puff pastry rounds and transfer to the prepared baking sheet. Spread 1 tablespoon of the chestnut puree over each round to within 1/2 inch of the edge. Freeze the rounds.
Preheat the oven to 400°. In a medium saucepan, combine the water, Armagnac, sugar and vanilla bean and bring to a simmer. Add the prunes and poach over moderately low heat until plumped, 15 to 20 minutes. Remove the prunes to a plate. Add the cranberries to the poaching liquid and cook until plumped, about 5 minutes. Remove to a plate. Simmer the poaching liquid until it reduces to a syrup, about 3 minutes. Strain the syrup.
Arrange the prunes and cranberries on the rounds and brush with some of the syrup. Bake for 25 minutes, or until the pastry is well browned and cooked through. Let cool slightly. Brush the tarts with the remaining syrup, top with a dollop of crème fraîche and serve.