Desalt the salt cod: Soak it in fresh cold water, refrigerated, for 36 to 48 hours, changing the water at least four times. Drain well.
Heat the oil in a medium saucepan over medium heat and add the leeks, garlic, and spring onions. Sauté until tender, 5 to 8 minutes, and add the potatoes. Cook, stirring, for a few minutes, until coated with oil, then add the smoked and desalted cod. Cook, stirring, for about 5 minutes until well incorporated, making sure not to brown the fish. Add the stock. Simmer until the potatoes are fork tender, about 20 minutes.
Remove from the heat and add the cream. Let stand for a few minutes, then transfer to a blender (it’s best to do this in batches). Don’t blend hot! Blend the mixture until smooth, about 30 seconds per batch, while drizzling in the truffle oil. Season lightly with salt. Taste and adjust seasoning with the pepper.
Serve ½ cup of the pureé in small glasses or bowls. Top with a few drops of parsley oil and ½ teaspoon of herring roe. Decorate with chervil and serve.