Cut the legs and thighs off the chicken carcass, then cut them in half at the knee joint. Heat up a large saucepan (it will need to be around 5-6 litres - big enough to hold the chicken comfortably), add half the olive oil and then the chicken thighs and legs and cook over medium heat until the chicken has browned all over. Remove the chicken but keep the pot on the heat. Add the garlic, shallots, carrots and lemongrass and fry until the shallots are coloured, stirring frequently. Return the legs and thighs to the pan along with the herbs, a few teaspoons of salt and the crown of the carcass (the body with the two breasts attached). Pour on enough cold water to cover the chicken by a few centimetres then bring to the boil. Turn to a simmer and cook with the lid on for 8 minutes. Remove the carcass using a pair of tongs, or two forks, and place it in a bowl. Turn the heat up to a gentle boil and continue to cook the legs and thighs for another 6 minutes. Return the carcass to the pan, put the lid on and turn the heat off. The chicken will continue to cook in the latent heat in the pot, and it will be cooked all the way through in 20-30 minutes.
To make the polenta, remove 650 ml of the stock and pass it through a sieve into a 2-litre pan along with the smoked salt, and bring to a rapid simmer. Put the sieved polenta into a jug (it makes it easier) then slowly pour it into the simmering stock, whisking gently but continuously until it has all been added. Turn the heat up to moderate and swap your whisk for a spoon or spatula, then cook for 1-2 minutes, stirring constantly to prevent lumps forming, then mix in the Manchego. Taste for seasoning, adding extra salt or Manchego if needed.
Bring a pan of lightly salted water to the boil, add the beans and peas and cook for 2 minutes or so, until just cooked, then drain. In a wide frying-pan or pot, place the sesame seeds, Sichuan pepper and pine nuts along with the remaining olive oil and cook over a moderate heat until the pine nuts are golden - stirring constantly. Once they’ve coloured, add the spinach and cook it until it wilts. Add the beans and peas to the pan and season with salt and freshly ground black pepper, give it a good toss and stir, then cook for a minute to warm it all through.