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Roll out the pastry on a lightly floured surface to about 0.5cm thick. Grate over a dusting of nutmeg using a fine grater, then scatter over the cinnamon in pinches. Roll the pastry a few more rolls to press in the spices. Cut out circles to line 6 x 10cm round, deep-ish individual tart tins, with a little overhang. Sit them on a baking sheet and chill for 30 mins.
Heat oven to 200C/180C fan/gas 6. Line the tart cases with small pieces of scrunched-up baking parchment, fill with baking beans and blind-bake for 15-20 mins until pale golden and set. Remove the paper and beans, and bake for a further 10-15 mins until biscuity. Cool, then trim the edges with a small, sharp serrated knife.
Reduce oven to 150C/130C fan/gas 2. Whisk together the eggs and sugar in a large bowl. Put the cream, milk and vanilla into a saucepan and bring to the boil. Pour onto the egg mixture, whisking as you go, then sieve into a jug. Divide the blackberries between the tins, then pour over the custard to fill as much as you can. Grate over some more nutmeg and bake for 20-30 mins. They’ll be ready when the top is set but the centres tremor slightly when the baking sheet is jiggled. Cool completely before eating.