Make the crème pâtissière. Heat the milk and cream together in a pan over a low heat until simmering.
Meanwhile, in a separate bowl whisk together the egg yolks, vanilla, caster sugar and cornflour, then pour the hot milk mixture over, whisking continuously until smooth.
Return the mixture to the pan, then whisk it over a low heat until thickened. Pour the crème pâtissière onto the baking tray and cover with cling film. Leave to cool completely.
Make the choux pastry. Pour 250ml of water into a pan and add the butter. Bring to the boil over a medium heat and stir to combine. Add the plain flour, then remove from the heat and beat vigorously with a wooden spoon until the mixture comes away from the sides of the pan.
Spread the mixture on a plate and leave to cool for 15 minutes. Meanwhile, heat the oven to 200°C/180°C fan/Gas 6. (400 °F)
Return the choux mixture to a bowl and add the beaten eggs a little at a time, until you reach a dropping consistency (the mixture will fall easily from the spoon in a blob).
Draw 18 lines, each 10cm long, on the paper lining your baking sheet. Turn over the baking paper so that the lines are on the underside.
Spoon the choux mixture into the large piping bag with the 1.25cm nozzle. Pipe 18 lines of choux on the lined baking sheet, using the pencil lines as a guide. Flatten any pointed ends with a damp finger. Bake for 40 minutes, until puffed and golden.
Skewer a hole in the end of each bun to allow the steam to escape and return to the oven for a further 5 minutes, then remove from the oven and transfer to a wire rack to cool completely.
While the buns are cooling, make the icing. Put all the ingredients in a bowl, then add enough water, a little at a time, to form a glossy, firm icing.
Spoon the crème pâtissière into the medium piping bag with the small nozzle. Insert the end of the nozzle into the steam hole and evenly fill each bun.
Use a spoon to spread icing over each bun and allow to set, then serve. (I dipped the top in.)