Peel and slice the ginger. Wash organic lime hot, dab dry and finely grate the peel. Squeeze all limes. Measure out 100 ml juice. Place the lime zest, prosecco, 100 g sugar and ginger in a pot. Bring everything to the boil covered and then simmer open for about 3 minutes.
Pour the ginger prosecco through a sieve into a clean ice container (at least 1 l capacity) with lid and let it cool open. Cover and freeze for at least 6 hours, stirring briefly every hour after 2 hours freezing time.
For the sugar rim, lightly crush the chilli and 1 tablespoon of sugar in a mortar and place on a saucer. Slightly moisten the edges of four glasses (approx. 250 ml each) (e.g. with some lime juice). Dip the edges in sugar-chili-mix. Place glasses in a cool place.
Let the granite thaw for about 20 minutes before serving. Scrape off with a spoon and serve in the chilled glasses.