Make the crumble by rubbing all the ingredients, except the chopped hazelnuts, together until crumbly.
Divide the pastry into 4 even pieces and roll out one at a time on a lightly floured surface to a thin round. Reserve half the crumble, and sprinkle the rest over the middles of the pastry. Arrange the blackberries on top, huddling in the centre. Fold or pinch up the pastry edges a little around the fruit, then scatter over the reserved crumble with the chopped hazelnuts. Carefully lift the galettes onto a baking sheet and chill for 30 minutes at least.
Preheat the oven to 200°C (180°C fan oven) Gas Mark 6. Bake the tarts for 20-25 minutes until the pastry is golden and crisp and the berries are oozing. Serve immediately with cream, yogurt or ice cream.