Rinse the rice well, then combine the milk and cardamom in a heavy saucepan over medium-high heat. Bring the mixture to a bubble, then reduce the heat to the point that the mixture just simmers gently. Cook, stirring occasionally, until the rice is very tender and the milk has been reduced by almost half, about 45 minutes to 50 minutes.
Stir in the sugar and 4 tablespoons of the pistachios and continue to cook, stirring more frequently now, until the mixture is the consistency of a thin porridge (it will continue to thicken as it cools), another 15 minutes or so. Remove from heat, add salt and adjust the seasoning with more sugar or a dash of ground cardamom if you like, then stir in the rose water. Serve room temperature or chilled, garnished with ground pistachios.