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Break the pastry into chunks and drop into a food processor. Drizzle over the vanilla paste and pulse until the vanilla is speckled through the pastry (the extract should be completely absorbed). Tip out onto a floured surface, bring together into a ball, then roll out to line a 23cm tart tin (leave any overhanging pastry as you will trim this away when the tart is baked). Chill for 30 mins.
Heat oven to 200C/180C fan/gas 6. Line the pastry with greaseproof paper. Fill with baking beans, bake blind for 15-20 mins, then remove the paper and beans and bake for 5-10 mins more until pale golden. Carefully spread caramel over the base and set aside while you make the filling. Lower oven to 180C/160C fan/gas 4.
Melt the chocolates in a bowl over a pan of barely simmering water, then stir in the melted butter. Whisk the eggs, yolks and sugar together with an electric whisk in a large mixing bowl for 10 mins, until pale and thick enough to leave a trail when the beaters are lifted up. Fold in the melted chocolate with a large metal spoon, then scrape into the tin.
Bake for 20-25 mins – the surface should be set and puffed but still with a slight wobble. Cool, then chill for at least 3 hrs or overnight, before dusting with icing sugar and serving.