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The tart can be made several hours ahead and served cold.
Preheat the oven to 170°C, fan 150°C, gas 3. Put the tomatoes, cut-side up, on a baking tray. Season and sprinkle with the sugar and roast them for 45-50 minutes in the preheated oven.
Meanwhile, make the pastry. Whiz the flour and butter in a food processor with a pinch of salt. Add enough water (about 2 tablespoons) to bring it together. Tip the pastry on to a lightly floured surface and shape it into a ball with your hands. Pat into a flattish disc and chill for 30 minutes.
When ready, take the tomatoes out of the oven and transfer to a board to cool. Increase the oven temperature to 200°C, fan 180°C, gas 6 and put the (washed) baking tray back in the oven to keep warm.
If time is short, make this with shop-bought shortcrust pastry, and if you want to use regular-sized tomatoes, cook them at the same temperature for 50-55 minutes.
On a lightly floured surface roll out the pastry and use it to line a 20cm tart tin that’s 4cm deep. Line with nonstick baking paper scattered with ceramic baking beans (or uncooked rice) and bake on the hot baking tray for 15 minutes. Remove the paper and beans and bake for a further 5 minutes or until the pastry is pale golden.
Whisk together the crème fraîche, eggs, Parmesan, paprika and a pinch of salt.
When the pastry case is ready, reduce the oven temperature to 180°C, fan 160°C, gas 4. Pour the Parmesan mixture into the pastry case and bake for 20-25 minutes. Serve barely warm, scattered with the slow-roasted tomatoes and basil.