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First make the pastry. Tip the flours into a food processor with ½ tsp salt and the diced butter. Pulse until you can’t feel any lumps, then tip in the walnuts. Mix the egg yolks with 3 tbsp cold water, then dribble this into the machine while you pulse again until the pastry comes together. Tip the pastry out onto a floured surface, lightly bring it together into a ball, then roll out and line a deep 20-23cm tart tin with overhang. The pastry may crack, but just patch it back together, then cover and chill for 1 hr.
To make the filling, melt the remaining butter in a large pan, then add the shallots and soften for 10-15 mins, until golden and squishy. Stir in the thyme for 1 min, then remove from the heat. Beat the eggs in a jug with the crème fraîche and cream. Crumble in the cheese and season with pepper and a small amount of salt.
Heat oven to 200C/180C fan/gas 6. Blind bake the pastry for 20 mins, remove the baking beans and paper, then bake for a further 15-20 mins until golden and sandy. Reduce the oven temp to 180C/160C fan/gas 4. Add the cooled onions to the cream mixture and pour into the case. Sit the fig halves on top, cut side up, sprinkle with some more thyme and bake on the middle shelf for 1 hr-1hr 10 mins until the tart is browning and has a slight wobble – the cheese middle will firm up on sitting. Cool for about 15-20 mins, then remove from tin and serve with a green salad.