For the soup, melt the butter in a heavy-based, lidded saucepan over a low to medium heat. Add all of the vegetables and fry gently for 4-5 minutes, or until just softened.
Add the mussels, wine and stock and bring the mixture to the boil. Cover the pan with the lid and reduce the heat until the mixture is simmering. Simmer for 2-3 minutes, or until the mussels have opened. (Discard any mussels that do not open during cooking.)
For the salsa verde, put all the herbs in a food processor and pulse until roughly chopped. Add the shallot, anchovies, capers, lemon juice, mustard and oil and blend to a rough purée. Season, to taste, with salt and freshly ground black pepper.
Remove the soup from the heat and stir in 2-3 tablespoons of the salsa verde.
Serve immediately, with an extra dollop of salsa verde on top of each portion. (Any remaining salsa verde can be decanted into an airtight container and covered with a thin layer of olive oil. It can be kept in the fridge for up to four days.)