Whisk together 1 cup of pomegranate juice and cornstarch until smooth. Set aside.
In a saucepan, over medium heat, combine remaining pomegranate juice and sugar. Bring to a simmer and stir until all sugar is dissolved, about 5 minutes.
Reduce heat to medium-low and add the cornstarch mixture, stirring constantly for about 5 minutes or until set. The mixture is set when it can lightly coat the back of a spoon.
Add rose water and pomegranate arils. Remove from heat and stir to combine.
Pour into 9-inch serving dish and let cool to room temperature. Transfer to refrigerator until set; about 6 to 8 hours.
Serve with pomegranate arils, chopped pistachios and rose petals.