Combine the sugar and water in a saucepan over a medium heat. Stir until the sugar dissolves and bring to the boil before reducing the heat to low and simmering for 5 minutes. Remove from the heat, add the mint leaves, lime juice and zest, and rum and cover and set aside to infuse for 20 minutes. Strain and set aside.
Place the chocolate in a heatproof bowl over a pot of simmering water and stir until melted.
Place the cream cheese and mascarpone in a food processor and process until smooth. Add the strained syrup and melted chocolate and process to combine.
Combine the crushed biscuits and melted butter and stir to combine. Divide half the mixture between 6 glasses and press into the base. Top with half the cheesecake mixture. Top this with the remaining biscuit mixture and then layer with the remaining cheesecake mixture. Refrigerate for 1 hour to set.
When ready to serve top with a dollop of cream, mint leaves and finger lime caviar.