Preheat the oven to 180C/360F/Gas 4.
Roll out the puff pastry to a rectangle slightly larger than a sheet of A4 paper.
Place the pastry on a greased baking sheet, cover and refrigerate for 30 minutes.
Peel, core and finely slice the apples and pears and toss with half the lime juice.
Using a hot, wet, sharp knife, cut the chèvre in half lengthways.
Finely slice the chèvre into thin, half-moon shapes.
Beat together the egg white and the milk.
Take the puff pastry rectangle and brush the egg white mixture around its edges.
Place alternate slices of apple and pear in neat lines across the rectangle, leaving a 2cm (¾in) gap of pastry around the edge.
Place the chèvre slices so that they overlap with the fruit slices.
Bake the fruit tart for 15-20 minutes until the pastry is crisp, the fruit is golden and the goats' cheese has browned.
Meanwhile, using a mortar and pestle, grind together the chilli and sugar to form a paste.
Mix in the remaining lime juice, olive oil, salt and freshly ground pepper and mix together well.
Once the tart is cooked, remove from the oven and allow to rest for five minutes.
Drizzle over the chilli lime dressing and serve with a green salad.
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James Martin is joined by chefs Tom Kitchin and Luke Matthews, and guest Mary Berry.