Grind the walnuts in a pestle and mortar until fine. Halve and deseed the chillies, then pop into a blender with 100ml of water and blitz to a purée.
Boil the potatoes in a large pan of boiling salted water for about 15 minutes, or until cooked through. Drain and steam-dry in a colander for a few minutes, then return to the pan, dress with oil and season.
Put a lug of oil in a small frying pan over a medium heat. Destone and tear in the olives and pick in the mint leaves. Fry until lightly crispy, then add to the potatoes.
Place the chicken between 2 sheets of greaseproof paper and bash with a rolling pin or a heavy pan until flattened and an even thickness. Season well, drizzle with oil and place in the fridge until needed.
Peel and finely chop the onion and garlic, then gently fry in a non-stick pan over a low heat with a good lug of oil for 20 minutes, or until soft and sticky.
Stir in the blitzed chilli and cook for a few more minutes before adding the breadcrumbs. Stir in the milk and cook for about 4 minutes, or until the sauce thickens, adding a splash of water, if needed.
Stir in the ground walnuts and finely grate in the Parmesan, simmer for a further 7 minutes, then season and keep warm while you cook the chicken.
Heat a griddle pan until screaming hot, then add the chicken, skin-side down. Cook for around 4 minutes, or until the skin is lovely and golden, then turn and cook on the other side for 3 to 4 minutes, or until cooked through.
Serve the chicken on the sauce with the potato salad on the side. Add a squeeze of lemon (if using) and some extra sliced chilli, if you like.