Bring the water and sugar to the boil in a small pan, reduce the heat and simmer for approx. 2 mins. Pour the syrup into a stainless steel bowl, allow to cool slightly. Puree the cucumber with the peppermint, pass through a sieve into the syrup. Cover and freeze the mixture for approx. 5 hrs., scrape the mixture four times with a fork until frozen.
Heat the cream in a pan; do not boil. Remove the pan from the heat, add the chocolate and stir until melted, leave to cool. Cover and chill in the fridge for approx. 5 hrs.
Using the whisk on a hand mixer, beat the chocolate cream until stiff. Transfer the mousse to a piping bag with a smooth nozzle (approx. 1 cm in diameter). Place the meringues in the glasses, pipe the mousse on top. Serve the granita on top of the mousse, serve immediately.