Line a baking sheet with baking paper. Place the butter, 50 g (2 oz) caster sugar, flour and most of the lime rind (reserving a little for decoration) in a food processor and pulse until the mixture comes together to form a dough.
Divide the mixture into 8 equal pieces and roll each piece into a ball. Place on the prepared baking sheet and flatten the biscuits with the back of a fork.
Bake in a preheated oven, 180°C (350°F), Gas Mark 4, for 10–15 minutes until golden. Transfer to a wire rack to cool.
While the biscuits are cooling, whip the cream with the remaining sugar, then fold in the strawberries.
Sandwich together 2 biscuits with some strawberry cream, then repeat with 6 more biscuits. Decorate with lime rind and a dusting of icing sugar. Serve any remaining strawberry cream separately.