Place the sugar, finely grated lime rind and juice in a small bowl and stir to dissolve the sugar.
Whip the cream with a hand-held electric whisk until it forms soft peaks. Slowly whisk in the cachaça or rum, then add the lime mixture. Whisk until thick and fluffy, then spoon into 4 glasses. Decorate with lime rind and serve with shortbread biscuits.