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Roll out the pastry on a lightly floured surface until large enough to line a 23cm loose-bottomed tart tin. Trim the excess pastry from around the edge, then line the pastry case with baking parchment, fill with baking beans and chill for 30 mins.
Heat oven to 200C/180C fan/gas 6. Bake the pastry case for 15 mins, then carefully lift out the parchment and beans, and bake for 5 mins more or until biscuity. Meanwhile, beat the eggs, cream, sugar and vanilla together, then strain into a jug.
Scatter the gooseberries into the pastry case, then pour in the vanilla custard mixture. Bake for 35-40 mins until the custard is set and the gooseberries are tender. Cool a little before serving, or cool completely and eat cold, dusted with icing sugar, if you like.