For the rhubarb ice cream, place the rhubarb pieces, 50g/2oz of the sugar and all of the water into a pan. Stir well and cover the pan with a lid.
Cook the rhubarb over a medium heat for 3-4 minutes, or until the rhubarb has softened, then remove the lid and continue to cook until it has broken down.
Meanwhile, in a bowl, whisk together the egg yolks and the remaining sugar until pale and fluffy.
In a separate pan, bring the milk, cream, vanilla pod and vanilla seeds to a simmer. When the milk mixture is just boiling, discard the vanilla pod (it can be washed and dried thoroughly, then reused in another recipe).
When the milk mixture is just boiling, pour it over the egg and sugar mixture, whisking thoroughly until the mixture is smooth and well combined.
Return the mixture to a clean pan and cook over a low to medium heat for 2-3 minutes, or until it is thick enough to coat the back of a spoon.
Add three-quarters of the softened rhubarb and stir well until combined. Transfer the mixture to an ice cream maker and churn for 40-50 minutes, or according to the manufacturer's instructions.
When the ice cream mixture is almost solid, transfer it to a freezable container.
Fold in the remaining softened rhubarb to form a ripple pattern, then freeze the ice cream for 3-4 hours, or until solid.
For the roasted rhubarb, preheat the oven to 200C/400F/Gas 6.
Place the rhubarb into a roasting tray, pour over the cider and add all of the remaining roasted rhubarb ingredients, including the vanilla pod. Transfer to the oven and roast for 8-10 minutes, or until the rhubarb stems are just tender.
Carefully remove the rhubarb pieces from the cooking liquid using a slotted spoon and set aside onto a plate to cool.
Bring the remaining cooking liquid to the boil in a pan. Boil for 2-3 minutes, or until the volume of liquid has reduced and thickened slightly. Set aside until ready to serve.
For the rhubarb tart, increase the oven temperature to 220C/425F/Gas 7.
In a separate saucepan, bring the milk and vanilla pod to the boil.
Meanwhile, in a bowl, whisk together the sugar and egg yolks until pale, fluffy and well combined.
Pour the hot milk mixture over the egg and sugar mixture and whisk together until smooth and well combined.
Return the mixture to a clean pan and bring to a simmer.
Add the cornflour, whisking continuously to remove any lumps. Continue whisking over a medium heat until the mixture is thick enough to coat the back of a spoon. Transfer the custard mixture to a bowl, cover with cling film to prevent a skin from forming, then set aside to cool.
Roll the puff pastry out onto a lightly floured work surface to a 0.5cm/¼in thickness. Using a cookie cutter or an upturned mug, cut four 15cm/6in discs from the pastry. Brush each disc all over with the beaten egg then prick several times with a fork. Transfer the discs to a baking sheet.
Spoon the cooled custard mixture into the centre of each pastry disc, leaving 1cm/½in free around the edge.
Arrange the roasted rhubarb stems on top of the custard mixture.
Bake the rhubarb tarts in the oven for 12-15 minutes, or until the pastry has risen and is golden-brown.
To serve, place a rhubarb tart into the centre of each of four serving plates. Place 1-2 scoops of rhubarb ice cream alongside. Drizzle over the reserved cider sauce.