Soak the salt cod in a large bowl of cold water for 48 hours, changing the water 5–6 times a day.
Drain the cod and put in a saucepan with the bay leaf, garlic and crushed chillies. Pour in enough milk to completely submerge the cod. Bring to the boil, then reduce the heat and simmer for 10 minutes. Remove the cod with a slotted spoon, reserving the poaching milk and garlic cloves, and leave until cool enough to handle. Break into flakes, removing and discarding the skin and any bones.
Process the cod with 5 tablespoons of the reserved poaching milk and the garlic cloves in a food processor until smooth. With the motor running, add the oil in a very slow, steady stream until incorporated.
Stir in the parsley, chopped fresh chilli and, if necessary, a little salt. Drizzle with oil and serve with the griddled or toasted bread.