Place the sugar, water and fresh mint into a microwave-safe dish.
Cook on full power for 1-2 minutes until the sugar has totally dissolved. Keep an eye on it to make sure the liquid doesn't bubble over.
Leave the minty simple syrup to cool to room temperature before storing in the fridge for at least one hour until chilled.
Stir together the cava, vodka, grapefruit juice and mint simple syrup together and serve immediately before the bubbles disappear.