Pour the cream into a saucepan, add the sugar and heat gently, stirring, until the sugar has dissolved. Bring to the boil and cook for 1 minute then take off the heat, stir in the lemon rind and gradually mix in the strained juice. Pour into a deep non-metallic dish and allow to cool.
To make the compôte, put the blackberries, sugar and water into a small saucepan. Cover and cook gently for 4–5 minutes until the blackberries are just cooked. Mix the cornflour with a little water to make a smooth paste. Stir into the blackberries and bring back to the boil, stirring until the sauce has cleared and thickened. Cover and allow to cool.
Freeze the cooled lemon custard for 4–5 hours until just firm and partially frozen. Reheat the compôte. Scoop the semi freddo into small bowls or glass tumblers using a hot dessertspoon. Spoon the warm compôte over the top and serve immediately with biscotti biscuits.
For chilled citrus pots with summer fruits, add 125 ml (4 fl oz) mixed lemon, lime and orange juice to the sweetened cream and lemon rind mixture. Chill until set, then serve with mixed summer fruits. This dessert is not frozen.