Combine rhubarb, water, honey, and sugar in a medium saucepan, bring to a boil, then reduce to a simmer and cook until rhubarb is soft, about 5 minutes.

Transfer rhubarb mixture to a blender and blend until smooth then strain through a fine mesh sieve into a large bowl. Stir in Prosecco, lemon juice, cardamom (if using), and salt.

Ladle mixture into 3 ice cube trays and freeze at least 3 hours or up to 5 days.

Meanwhile, freeze a medium glass or metal bowl, food processor workbowl, and food processor blade at least 30 minutes. Attach workbowl and blade to food processor.

Working quickly, and with one tray at a time, use a dinner knife to loosen the cubes out of the trays and into the chilled workbowl. Pulse cubes until mixture is smooth and creamy, 18–20 pulses. Transfer mixture to chilled bowl and freeze while processing remaining 2 trays. Serve immediately, or transfer to an airtight container and freeze until ready to serve.