Prepare the rose syrup. In a medium saucepan over medium-high heat, stir together the sugar, water, and a very small pinch of salt (about 1/4 teaspoon). Bring to a boil, then reduce the heat and simmer for 5 minutes, stirring regularly. Remove from the heat and stir in the rosewater and lime juice. Cool the syrup completely, then transfer to a freezer safe dish and freeze (uncovered) for 30 minutes.

While the syrup cools, cook the rice noodles. Fill a medium saucepan with water and bring to a boil over high heat. Set a bowl with ice water nearby. Once boiling, add the noodles and cook according to the package instructions. Drain and transfer to the ice water to prevent further cooking and sticking. Once the noodles have fully cooled, drain once more and place them in a bowl. Use kitchen scissors to cut the noodles into pieces, approximately 1 inch in length. Set aside.

Add the noodles to the rose syrup: Remove the syrup from the freezer and stir in the noodles. Return (uncovered) to the freezer for 1 hour and 30 minutes.

Scrape and stir to create the granita-like texture: remove the mixture from the freezer. Use a fork to scrape the mixture from the sides into the middle of the dish and then stir the mixture. This process avoids icy chunks being formed and creates the granita-style texture. Place the mixture back in the freezer for 1 hour before repeating scraping and stirring. Repeat the process two more times. The texture should be coarse and icy from the frozen syrup, punctuated with crispy noodles.

Serve the faloodeh: Scrape the noodles with a fork and divide between small bowls and add a wedge of lime alongside. If you like, garnish with a drizzle of cherry syrup and scattering of pistachio slivers and/or pomegranate seeds.