In a pitcher, combine the limoncello and mint. Use a long wooden spoon to gently bruise the mint. Add both melons and stir to combine, lightly pressing the melons as you stir. Add the pinot grigio.

Cover and chill the sangria until ready to serve, at least an hour or overnight. Serve in glasses filled with ice, making sure to scoop some of the melon into each glass, and garnish with mint sprigs.