Place the saffron on a piece of foil. Fold some of the foil over the saffron and crush it with a rolling pin or wooden potato masher. Put the crushed saffron in a small cup. Add the hot milk, cardamom, and sugar. Mix with a toothpick or the handle of a small spoon and set aside for 3 hours.
Put the rice in a bowl and wash in several changes of water. Drain, add fresh water to cover generously, and leave to soak for 30 minutes. Drain.
Pour the oil in a heavy, lidded pan that will just hold the cooked rice comfortably and set over medium heat. When the oil is hot, put in the cinnamon sticks. Stir for 10 seconds, then add the rice. Reduce the heat to medium-low and stir the rice around until the grain looks translucent, about 2 minutes. Add 2 2/3 cups of water and the salt. Bring to a boil. Cover. Reduce the heat to very, very low and cook for 25 minutes. Turn off the heat. Lift the lid and quickly dribble the saffron milk in any haphazard pattern. Quickly cover again and leave for 10 minutes. Mix the rice very delicately with a slotted spoon before serving.
Recipe courtesy Madhur Jaffrey, from "Curries to Kebabs: Recipes from the Indian Spice Kitchen", Clarkson Potter, 2003