Preheat the oven to 230C/445F/Gas 8.
Line a baking tray with baking parchment.
Trim the chicory, removing any brown leaves, but do not cut off the stem at the bottom, because this holds the chicory together. Cut the chicory in half lengthways, then cut each half into four equal pieces lengthways. Place the chicory onto the baking sheet and drizzle with the sherry vinegar.
Dot the chicory generously with little knobs of butter and season well with salt and freshly ground black pepper.
Sprinkle the chicory with caster sugar and cook in the oven for 15 minutes.
Check the chicory after 15 minutes. If it has started to brown, turn it over in the melted butter and return it to the oven. If not, allow to cook for 4-5 more minutes before turning.
When the chicory is almost golden-brown all over, place the hazelnuts or walnuts for the salad onto a baking tray and roast for 3-4 minutes. Remove and allow to cool, then roughly chop.
Season the pigeon breasts with salt and freshly ground black pepper.
Melt the butter in a frying pan over a medium heat. Add the pigeon breasts and cook for 2-3 minutes, until browned, then turn over and cook for a further 2-3 minutes, or until cooked to your liking. Set aside to rest for 3-4 minutes, then carve each pigeon breast into four slices.
For the dressing, place the walnut oil, vinegar and mustard into a bowl and mix well. Season, to taste, with salt and freshly ground black pepper.
To serve, place the mixed lettuce leaves into a bowl and add the chicory. Mix gently, then add equal amounts of salad onto each plate.
Place a sliced pigeon breast onto each salad and drizzle with the dressing. Sprinkle each salad with equal amounts of sliced pickled walnuts and the chopped roasted nuts.