Put the chicken, water, and salt in a saucepan. Bring to the boil, cover, lower heat, and simmer gently until the chicken is soft. When the chicken is cool enough to handle, discard the skin and remove the flesh from the bones, shredding it finely by hand. Put back into chicken stock.
Prepare seasoning paste by processing all ingredients listed below seasoning paste. Add a little of the oil if needed to keep the mixture turning.
Heat the oil in a saucepan with a heavy base, then add the seasoning paste and stir-fry over low-medium heat until fragrant, about 4 minutes. Add the reserved chicken stock with the chicken pieces and bring to the boil. Add the coconut milk and kaffir lime leaves, then bring gently to the boil, stirring. Taste and add a little chicken stock powder if desired. Simmer with the pan uncovered for 5 minutes.
In between, slice the 2 shallots very thinly and evenly. Heat enough vegetable oil to cover the shallots. When it is just warm, not hot, add the sliced shallots and cook over low heat, stirring frequently, until they are golden brown and crisp. It is important to keep the temperature low otherwise the shallots will brown before they are cooked. The process may take around 8 minutes. Lift out and dry on paper towel. The flavoured oil can be kept for frying or used as a seasoning oil.
To serve, divide the noodles between four large bowls and pour the chicken stock over. Divide the sliced potatoes, egg quarters, bean sprouts, chopped coriander and crispy shallots.
Serve with a lime wedge and put a small dish of sambal oelek onto the table, so that your guests can spice up the dish if desired.