To desalinate the cod, rinse it, then place it in a container with plenty of water. You need to make sure the skin is facing up (if it’s on the bottom the salt won’t be released). Leave in the fridge for 24 hours, rinsing and changing the water three times in total.
Remove the salt cod from its final soak of water and dry with kitchen paper. Remove the skin and cut into bite-size pieces. Cover with the olive oil, pepper (salt isn’t necessary here!), garlic and parsley and leave to marinate overnight.
Half an hour before you’re ready to eat, take the salt cod from the fridge to give it time to come to room temperature.
Cut the tomatoes into wedges and put them on the plate you are going to serve the salad on. Season with salt, then top with the marinated cod pieces.
Just before eating (otherwise they will become mushy), pit the olives and mix with the capers, shallots, tarragon, olive oil, vinegar and a little white pepper. Scatter the olive dressing over the cod and tomatoes, and serve.