This is a very typical Cuban dessert, rooted in Spanish culinary traditions. The secret to this dessert is to cook the rice perfectly—until it is quite soft, but doesn’t lose its form—and then add the milk. Otherwise, the casein in the milk would prevent the rice from continuing to soften.
In a large pot, combine the rice, cinnamon stick, lime rind, and 5 1⁄2 cups (44 fl oz/1.3 liters) water. Cover and cook over medium heat until tender and fluffy, about 45 minutes. Add the sweetened condensed milk, evaporated milk, salt, and sugar and stir. Continue to cook, stirring occasionally so that the rice doesn’t stick to the bottom until the rice has absorbed the milk and sugar, about 30 minutes. Reduce the heat to low and cook, stirring constantly, until the rice pudding thickens, about 10 minutes, Pour it into a large serving dish while still hot, and sprinkle with cinnamon. Refrigerate for 2 hours. Serve cold on small dessert plates.