Combine the rice with milk, water and cardamom in a heavy medium-large saucepan over medium heat. Bring to a vigorous simmer, then reduce the heat to a gentle simmer. Cook uncovered, stirring occasionally, until the rice is very tender and the milk has been reduced by almost ½, about 30 minutes.

Stir in sugar and continue to cook, stirring more frequently, until the pudding is the consistency of a thin porridge (it will thicken as it cools), another 10 minutes or so. Remove from heat, add salt and then stir in the rose water.

Serve room temperature or chilled, topped with the slivered almonds and optional dried or fresh rose petals.