Place the rice in a large bowl; pour lukewarm water, stir and pour off the water. Repeat four times or until water runs clear. Soak the rice in water for 4 hours.
Then drain the rice. Place the rice and water in a deep pot. Cook uncovered over medium heat until rice slightly softens, about 20 minutes. Add milk and sugar. Cover the pot and simmer over low heat until the mixture thickens, about 2 hours (stir occasionally to prevent rice from sticking to the bottom). Then add the rosewater and heavy cream; stir well and cook for 10 minutes.
Pour into individual dessert dishes and garnish with slivered pistachios. Serve Shir Berenj cold or hot with jam, syrup or more sugar.