Combine water, sugar, and rosemary leaves in a small saucepan. Bring to a boil, stirring until sugar dissolves. Reduce heat to low; let simmer for 1 minute. Remove from heat and let syrup steep, about 30 minutes.
Strain syrup into a sterilized glass jar. Cover and refrigerate until completely chilled, at least 20 minutes.
Drop sorbet into the bottom of a champagne flute. Pour 1 fluid ounce rosemary syrup and gin on top. Pour in Prosecco very slowly so that it does not overflow. Garnish with 1 cranberry and sprig of rosemary.