Put 175g (6oz) condensed milk, cream, zest and juice from 2 limes and roughly chopped ginger in a food processor with a pinch of salt. Whizz until mixture thickens, then pour into a 1 litre (13⁄4 pints) plastic container and freeze for at least 6 hours or overnight.
To make the sauce, warm remaining condensed milk, finely chopped ginger, ginger syrup and milk in a pan. Add chocolate chunks, stirring until they melt. Stir in remaining lime zest and juice and beat until combined.
Place 2 scoops of ice cream in each bowl and spoon over hot chocolate sauce. It will set on the ice cream.
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