Add rice to a saucepan and cover with water. Bring to the boil and cook for 2 to 3 minutes, then drain.
Meanwhile, bring the milk and vanilla to the boil in another saucepan. Drain the rice and pour it into the milk. Reduce the heat to low and cook the rice until tender and the milk is absorbed, about 45 minutes. Stir occasionally to be sure the rice is not sticking.
Preheat the oven to 150 C / Gas 2.
Stir in the sugar. Remove from the heat and stir the eggs into the rice mixture. Pour the mixture into 4 individual ramekins.
Bake in the preheated oven until a skewer inserted near the centre comes out clean, about 10 minutes. Chill for 2 hours in the fridge before serving.
If desired, you can add a handful of sultanas or raisins to the mixture whilst the rice and milk are simmering. If you don't have a vanilla pod, use 2 to 3 teaspoons of vanilla extract instead.