Add lime juice, sugar and mint leaves to a tall cocktail glass. Muddle gently to release the oil from the mint leaves and macerate the sugar. Don't over-muddle – if the mint is too bruised, it will start to taste bitter.
Fill the glass with ice, then pour in the passion fruit juice, lime juice, and rum. Stir well to combine. Optional: garnish with a passion fruit half and a sprig of mint.