Heat 80 ml (2½ fl oz/¹⁄³ cup) of the olive oil in a large wide saucepan with a tight-fitting lid, which is large enough to fit the mussels, over medium heat. Add the onion and garlic and sauté for 5 minutes or until soft.
Increase the heat to high, then add the mussels, wine and saffron with its soaking liquid and cover with the lid. Cook, shaking frequently for 5 minutes or until the mussels begin to open. Remove from the heat and strain the mussels into a sieve placed over a bowl. If your pan isn’t quite big enough to fit all the mussels comfortably, you may find you need to cook the mussels in two batches, which is fine. Simply scoop the first batch of cooked mussels out with a mesh strainer and keep aside while you cook the second batch. Strain the mussel broth through a fine sieve, leaving any gritty bits behind.
Season the fish with sea salt. Heat the remaining olive oil in a heavy-based, deep-sided frying pan over medium heat. Add the fish pieces and cook, without turning for 1 minute. Add the mussel broth and bring to a simmer. Cook the fish for a further 2 minutes, then turn over. Add the mussels and cook for 2 minutes or until the fish is just cooked.
Add the butter and gently stir through. Sprinkle the stew with the parsley and add a grind of white pepper.
To serve, place the pan on the table with a ladle and bowls for everyone, or serve in one beautiful big bowl to share among the guests. Serve with crusty bread on the side.