Warm 1 tbsp olive oil in a large, heavy bottomed pot over a medium heat. Add the chicken and sear on one side, untouched, for 4 minutes, then turn over and sear on the other side for 4 minutes. Remove from the pan and cover with foil, then set aside.
Blitz the crackers in a food processor until they're fine crumbs. Combine the eggs, soda water and all the pan juices left from searing the chicken in a large mixing bowl. Add the cracker crumbs, season well, then mix until completely combined. Leave in the fridge uncovered for 15 minutes.
Meanwhile, wipe the pan clean and add the remaining oil. Add the carrots and celery and cook on a medium heat for 5 minutes until softened slightly. Add the stock plus 750ml of water and bring to a boil, then cover and simmer. Remove the cracker mix from the fridge and, with wet hands, shape into 18 balls. Add the balls to the pot of vegetables and stock, cover and leave to simmer for 15 minutes.
Take the chicken thighs and use two forks to shred them. Remove the lid from the pot and add the chicken, spaghetti and sliced green beans. Replace the lid and leaving to simmer for another 8-10 minutes, or until the spaghetti is just cooked.
Just before serving, stir through the dill, parsley and a squeeze of lemon juice, then season to taste.