Put a coupe glass in the freezer, to chill whilst you continue with the recipe.
Start by making the grapefruit sorbet. Combine the sugar and 400ml of water in a saucepan, then bring the pan to a boil over a medium heat to dissolve the sugar. Remove from the heat and let it cool completely.
Once the sugar syrup is cool, add the grapefruit zest, grapefruit juice and lemon juice and give everything a good stir. Pour the mixture into your ice cream maker (whichever you have - have a look at its instructions first!), and churn until firm and frozen. Transfer to an airtight container and freeze for an hour, to let it properly solidify.
To make your sgroppino, combine two generous scoops of the grapefruit sorbet (about 100g, if you want to be precise), vodka and prosecco in a bowl. Mash the liquid into the sorbet with a fork, until you have something that is fluffy and slushy-like in consistency.
Pour the sgroppino into your chilled coupe glass, garnishing with a peeling of grapefruit zest, if you like.