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To make the pizza dough, combine the flour, yeast and a big pinch of salt in a large bowl. Pour in 120ml warm water and knead together with well-floured hands to form a smooth dough. Put the dough back in its bowl, cover with a tea towel and leave somewhere warm to double in size. Can be made the night before and kept chilled overnight.
For the buttermilk dressing, whisk together all the ingredients, adding lemon juice and some seasoning to taste. The dressing can be made the day before.
Get your barbecue searingly hot. Brush the broccoli, spring onions and the cut side of the lettuce with a little oil, then put all the vegetables on the barbecue and cook until charred – broccoli will take the longest, between 8-10 mins. Have a plate ready so you can remove them when they’re cooked.
On a lightly floured surface, roll the pizza dough into a circle, about 30cm in diameter. Flour a large piece of foil, put the dough on top and carefully place on the barbecue. Put the lid on the barbecue and cook the dough, with the lid on throughout, for 6-8 mins, flipping halfway, or until cooked through – it may take slightly longer if your barbecue has lost some heat. Pile the charred veg on top of the dough, drizzle over some of the dressing (leaving some to dip the crusts), then scatter over the toasted walnuts and lemon zest to serve.