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Heat oven to 220C/200C fan/gas 7. Heat the olive oil in a large frying pan, then add the butter. Once sizzling, add the leeks and cook over a medium heat until softened but not coloured. Stir in the thyme and half the lemon zest, then increase the heat. Add the lemon juice and cook for about 30 secs until the lemon juice reduces, then season well. Remove from the heat and cool slightly.
Unroll the pastry and lay on a baking sheet lined with baking parchment. Lightly mark a 1cm border around the edges with the tip of a sharp knife, then prick the base all over with a fork.
Spread the lemony leeks on top of the pastry, within the border. Crumble over the cheese, scatter with the walnuts, then season with pepper. Drizzle with some olive oil, brushing the edges with a little oil as well. Put tart in the oven for 15-20 mins until the pastry puffs up around the edges and is golden brown. Scatter with parsley and the remaining lemon zest. Serve hot, warm or cool.