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For the dressing, combine the olives, tomatoes and vinegar with seasoning and enough of the oil to bind. Set aside, then add the basil just before serving.
Sieve the flours with a pinch of salt into a large bowl and make a well in the centre. Pour in the water and stir to combine. Do not overbeat the mixture – it should be just combined and can have a few lumps.
Drain and pat the mozzarella balls dry, tear into small pieces, then season. To stuff the flowers, open the petals, pop in some mozzarella, then gently twist the petals to re-seal them.
Heat the sunflower oil in a large pan until a cube of bread browns in 20 secs. Drop the flowers into the batter, then remove, shaking off excess. Fry in batches of 2 or 3 until lightly golden, drain on kitchen paper and season with a little salt. Keep warm in a low oven as you cook the rest. Pile onto a platter and drizzle with the dressing.