Bring 2 cups of the water and the sugar to a simmer in a saucepan. Stir until the sugar dissolves, then cool completely.
Stir in the rosewater and lime juice.
Cook and Freeze:
Boil the remaining water. Add the rice vermicelli and cook until tender according to the package directions. Drain and rinse under cold water.
Stir the noodles into the chilled syrup and pour into a shallow freezer-safe dish. Freeze for 60 minutes, stirring with a fork every 20 minutes to keep the noodles separated.
Serve:
Spoon the faloodeh into chilled bowls and finish with pistachios, rose petals, and lime wedges.
Notes
Use culinary rosewater rather than cosmetic rosewater, which is not suitable for cooking.
A little sour cherry syrup makes a beautiful and traditional contrast to the rosewater.