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Preheat oven to 200°C/400°F/Gas Mark 6
Unwrap the puff pastry and using a 5cm cutter, cut out 20 rounds. Use a slightly smaller cutter to make a light dent in the pastry, creating a rim. Use a fork to make a few pricks in the centre of the pastry to stop it from rising.
Place the pastry discs on a baking sheet and brush all over with the egg. Crumble the goat's cheese in the centre of each tartlet and scatter the olives over the top.
Cook for 15-20 minutes until pastry is puffed and golden brown. Sprinkle with the parsley and serve.