How to Make It
In a large saucepan, combine the rice with the water, salt and cinnamon stick and bring to a boil. Cover and cook over moderately low heat until the liquid is absorbed but the rice is not quite tender, about 15 minutes. Add the milk, sugar and lime zest and bring to a boil over high heat. Reduce the heat to moderate and cook, stirring frequently, until the rice is tender but firm and suspended in thick, creamy liquid, about 10 minutes. Remove the rice pudding from the heat and discard the cinnamon stick.
Stir the vanilla and the dried apricots into the rice pudding. Transfer to a shallow bowl, cover with plastic wrap and refrigerate until chilled, about 2 hours. Just before serving, stir in the heavy cream.