Soak the rice, poppy seeds, and almonds for 4 hours. Drain and grind along with coconut.
Make a syrup using 2 cups water and 1 cup jaggery. Add the coconut-poppyseed paste to the syrup. Add saffron and cardamom powder. Bring the payasa to a boil, and cook till it thickens, stirring constantly.
If the payasa is too thick, thin it out with some milk or water, or a little of both. Serve hot, warm, or cold.