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In a saucepan, add the boiled chestnuts, sugar, vanilla extract, milk and water.
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Boil, and then reduce to a rolling simmer without a lid for 25-30 minutes.
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As soon as the liquid level reduces and there is about 2 cm of liquid left in the saucepan, remove from heat.
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Transfer the contents of the saucepan to food processor and beat until all of the ingredients are completely combined and puréed. If you find that the purée is very thick, you can add a touch more water to help it smooth out. But remember, you do want a thicker purée, not too creamy a mixture, or else it won't pipe through your potato ricer.
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(If you don't have a potato ricer and are planning on just spooning the purée gently over the set ganache, then it is alright to have it be a bit creamier. But still, don't let it become soupy.)
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Transfer to a bowl and store in the fridge till needed. This will keep in the fridge for 10 days, in a well sealed container.
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When ready, using two cups of the prepared purée, take spoonfuls and your potato ricer, and push the purée through onto the chocolate ganache layer. Move the ricer around to have the purée land in layers evenly over the shell. Continue till about two cups have been used. You will have leftover purée. Feel free to use it on toast, stuffed in crepes etc.
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Alternately, you can gently spoon and smooth the chestnut purée over the chocolate ganache till you have about 3/4- 1 inch of filling spread out.