Place the milk, sugar, split vanilla pod and the butter in a saucepan and bring to the boil. Remove from the heat and allow to cool at room temperature.
Sift the flour into a large bowl and make a well in the centre. Break the eggs (the yolks and the whole egg) into the centre of the well. Mix gently, gradually incorporating the flour into the eggs. Add the rum, mix well and then allow to rest for at least 24 hours.
Preheat the oven to 210°C.
Fill the moulds to 4/5, transfer to the oven and cook for 6 minutes at 210°C. Then lower the temperature to 180°C and cook for 5 minutes. Check that the cannelé are cooked and allow to cool in the moulds before turning out to serve.
«These little cakes are particularly flavoursome and delicious when served warm!»