Mix pistachios with syrup and rose water in large bowl. Set aside.
In a saucepan over medium heat, combine the rice, sugar, milk, cream, water, and vanilla and stir until combined. Bring to a boil. Reduce heat and simmer for 40 minutes, stirring constantly, until rice is cooked.
Layer pistachio mixture alternatively with rice pudding to fill a glass serving bowl. Refrigerate until well chilled.
