With a serrated small knife, cut an X in each chestnut. Place chestnuts in a saucepan, cover with water and bring to the boil. Cook till the chestnuts can be easily pierced with a knife, about 15 minutes. Peel while still warm, making sure to remove all of the thin fibrous inner skin.
In a saucepan bring half of the sugar with the vanilla bean and rum to the boil and cook, stirring, till it turns into a thick caramel like syrup. Remove from the heat and let cool.
In a bowl beat ricotta cheese, eggs and remaining sugar till smooth. Add orange peel and vanilla extract.
Pulse chestnuts in the food processor till finely chopped but not paste like. Add a little of the ricotta mixture if the blade runs Stir chestnuts with the ricotta mixture.
Preheat oven to 175 C / Gas 4. Line a 26cm springform tin with greaseproof paper and grease the sides very well. Add mixture and back in your preheated oven for 1 hour. Reduce heat to 160 C / Gas 3 and bake for a further 10 minutes.
Let cool slightly then unmould and let cool on a wire rack till cooled completely. Refrigerate and eat within in the next two days.