Combine sugar, water and vanilla bean and seeds in a small saucepan and cook until the sugar is completely dissolved. Add the plums and cook until very soft. Transfer the mixture to a food processor and process until smooth.
Spoon a tablespoon of the puree into each of 4 champagne flutes and fill to the top with Prosecco. Garnish each glass with a plum slice and a mint sprig.
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