Mix the milk, caster sugar, butter, vanilla sugar, lemon zest and cinnamon stick in a saucepan over medium to high heat.

Heat until small bubbles appear on the edges of the pan, then remove the pan from the heat and let cool for 30 minutes.

Meanwhile, in another large non-stick pan, bring water to a boil. Add the rice and salt and lower the heat.

Cook over low heat for 15 to 20 minutes until the rice is tender.
Drain the rice.

Place the saucepan containing the milk mixture over medium heat and simmer. Add the rice and, stirring very regularly, simmer uncovered for about 15 to 20 minutes, until thickened.
Remove the cinnamon stick.

Divide the hot milk rice into bowls and serve sprinkled with cinnamon.