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Heat oven to 200C/180C fan/gas 6. Remove the skin from the chicken and set aside. Cover the chicken with cling film and bash out to flatten slightly, then put in a large bowl with half of the lemon juice, 1 garlic clove, a drizzle of oil and some salt and pepper. Set aside.
If you’re making the crackling, lay the chicken skin on a baking sheet lined with baking parchment and sprinkle with sea salt. Put another piece of baking parchment on top, then weigh it down with a baking tray. Roast for 25-30 mins until crisp and golden.
Meanwhile, trim the crusts off the sourdough and tear the centre into pieces. Tip onto a baking tray, drizzle with the rest of the olive oil and finely grate over 15g of the parmesan. Toss everything together so the bread is completely coated in oil and cheese. Bake in the oven for 15-25 mins with the crackling (if making), tossing a few times, until golden and crunchy. The croutons and crackling can be prepared a day ahead and kept in an airtight container.
For the dressing, use a pestle and mortar to crush the remaining garlic to a paste, then mash in the anchovies. Spoon into a bowl and finely grate in 10g parmesan, then add the remaining lemon juice, mayo and mustard. Gradually stir in 4 tbsp oil. Can be made three hrs ahead.
Heat a griddle pan until smoking. Griddle the chicken for 4-5 mins on each side until just cooked, then set aside. Trim and discard any limp outside lettuce leaves and trim the rest into bite-sized lengths. Slice the chicken into pieces and use a peeler to shave the remaining parmesan, grating the final stump that can’t be shaved.
To serve, tip the lettuce, croutons, chicken and cheese into a large salad bowl and drizzle with most of the dressing. Toss everything together well (the easiest way is with your hands), then drizzle with more dressing, scatter with the crackling and serve.