Preheat the oven to 150C/300F/Gas 2.
Rinse the rice in cold water to remove the dusty starch from the surface – this will prevent the pudding becoming too thick.
Place the drained rice in a large saucepan with the milk, sugar and vanilla syrup.
Bring to the boil then turn the heat down and simmer very gently, stirring every five minutes, for 25 minutes.
Simmer for five more minutes, stirring slowly all the time to prevent the rice from sticking to the bottom of the pan.
Remove from the heat and pour into a shallow 2000ml/3½ pint ovenproof dish.
Bake in the oven for 30 minutes and then leave to rest for at least one hour - this will allow the creamy texture to develop.
Sprinkle the surface of the pudding with sifted icing sugar and serve warm.
To serve cold, preheat the grill to its highest setting. Sprinkle the cold pudding evenly with caster sugar, using a fine sieve, and place under the grill for 2-3 minutes. Cool for 10 minutes then serve.