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COMBINE 125 gram sugar and 125 ml water in the small saucepan and bring to a boil. FILL a bowl with cold water and soak the gelatin leaves in the water. The sugar-water is done as soon as the sugar has dissolved.
SQUEEZE any excess water from the gelatin leaves and dissolve them in the warm sugar-water (simple syrup) GRATE the limes and juice them. COMBINE 80 gram of cane sugar and 325 ml water with the lime juice and zest.
ADD cachaça rum and the simple syrup and let the mixture cool off completely.
POUR the mixture in the ice cream machine and set it on for about 40 minutes, the exact time depends on the machine. TRANSFER the sorbet into an airtight container and set in the freezer.
You can also serve it straight from the machine, but it will be quite soft. Enjoy!