Line the base and sides of a 20-22cm square cake tin with cling film. Finely grate the zest from the limes and set aside. Squeeze the juice and pour into a pan with the sugar and blueberries. Heat gently to dissolve the sugar, then simmer for 1-2 mins until the blueberries are slightly softened. Remove with a slotted spoon and put in a bowl. Boil the juice for 1-2 mins until it is slightly syrupy, then pour over the blueberries and leave to cool.
Whisk the egg whites until stiff, then gradually whisk in the icing sugar until the meringue is stiff and marshmallow-like in texture. Beat the mascarpone in a large bowl with the lime zest and vanilla. Whip the cream until it just holds its shape, then fold into the mascarpone. Fold in the meringue using the whisk blades.
Break up the amaretti biscuits between your fingers into a bowl to make crumbs. Melt the butter and add to the biscuit crumbs, mixing well.
Spoon the blueberries and their juices into the base of the prepared tin. Spoon the cheesecake mixture evenly over the top, then smooth with the back of a metal spoon to level the mixture. Spoon the amaretti crumbs evenly over the top, pressing down lightly with your hands. Freeze the cheesecake for at least 4 hrs – or overnight is better. Can be frozen for up to two weeks before serving.
To serve, transfer the cheesecake to the fridge for 30 mins. Turn out onto a flat serving plate and peel off the cling film. Serve cut into generous slices.