In a medium saucepan, combine the sugar, water, and Aperol. Bring it to a simmer and cook it for 4-5 minutes (you want to cook off a bit of the alcohol so it will actually freeze). Cool the mixture to room temperature.
Puree the strawberries with the Aperol syrup in a blender or food processor until smooth. Strain to remove the pulp and seeds. (If desired. This step is not totally necessary, but the pulp and seeds will lead to a less-smooth texture).
Gently whisk the strawberry-Aperol mixture with the lemon juice, orange juice, and Prosecco. Pour the mixture into a metal or glass baking pan.
Freeze for 2 hours, and then scrape the mixture with a fork. Scrape the mixture every hour for another 3-4 hours, or until the mixture resembles shaved ice. Cover with wrap until ready to serve. You can serve the granita with whipped cream and fruit, but I prefer it plain. Enjoy!