Chop the shallot very finely. Steam in the butter until soft. Extinguish with milk and fish stock. Bring to the boil. Knead butter and flour well with a fork. Add to the soup one piece at a time until it thickens. Season with salt, pepper and a few drops of lime juice.
Cut both kinds of fish into not too small cubes. Add to soup and let sit for about two minutes. Arrange in heated soup bowls. Cut chives directly on top with scissors. Serve immediately.