• to make the pastry
• Put the butter, flour and icing sugar in a food processor and process until the mixture forms fine crumbs.
• Add the beaten egg and process briefly, adding a few drops of chilled water if necessary for the dough to come together in a ball.
• Wrap dough in clingfilm and chill for 30 minutes.
• Roll pastry into a 30.5 cm (12 inch) diameter circle and use to line a 20.5 cm (8 inch) diameter, 5 cm (2 inch) deep loose-bottom tart tin. Chill for 20 minutes.
• Line with greaseproof paper and baking beans and bake at 200°C (400°F/ gas 6) for 15 minutes.
• Remove paper and beans. Return to the oven for 10-15 minutes, then brush with beaten egg white; return to oven for 2-3 minutes.

to make the filling

• Whisk the eggs gently for 30 seconds, then add the sugar and cream and whisk until evenly combined.
• Finally, whisk in the lemon and lime juice and the grated lime rind. The mixture will thicken suddenly.
• Pour mixture into the cooked pastry case. Bake at 150°C (300°F/gas 2) for 1 hour or until just set.
• To stop the custard cracking, cover the surface with tin foil, cut to fit exactly. Cool in the tin for 20 minutes, then unmould.
• Remove tin foil when the tart is completely cool.

to make the berry ice

• Dissolve the sugar and 100 ml (4 fl oz) water over a low heat.
• In a food processor, process the hot syrup and berries to form a puree. Freeze until needed.
• To make the candied limes, use a sharp serrated knife to cut the limes into thin slices.
• Dissolve the sugar and 100 ml (4 fl oz) water over a low heat, then add the lime slices.
• Poach for 15 minutes then drain, reserving the syrup. Cool.
• To caramelise the surface, cut the tart into eight pieces and place on a baking sheet. Freeze for 1 hour.
• Cover the pastry edges with foil to stop them burning.
• Dust each slice with sieved icing sugar and place the baking sheet under a hot grill for 2-4 minutes until the icing caramelises.
• Serve with the sorbet and lime slices, sprinkled with lime rind and drizzled with the reserved lime syrup