1. Soak the anchovies in the milk for 30 minutes.
  2. Rinse the mussels under cold running water and remove the broken ones.
  3. Divide the mussels among the two steamer inserts.
  4. Bring water to the boil in a saucepan, making sure there is at least 1 inch between the water and the steamer insert.
  5. Place both the steamer inserts with the mussels on top of one another above the boiling water and cover with the lid.
  6. Steam the mussels for 8-10 minutes until all the shells are open.
  7. Meanwhile, heat the butter together with the oil in a frying pan and fry the shallots and garlic for approx. 2-3 minutes.
  8. Add the basil and three quarters of the parsley and fry gently.
  9. Chop the anchovies finely and stir the finely chopped fish into the shallot mixture.
  10. Allow the anchovies to melt while stirring.
  11. Stir in the wine and wine vinegar and dilute the sauce with a few spoons of the liquid from the steamer.
  12. Divide the mussels among deep bowls or plates and spoon over the sauce.
  13. Season with freshly ground pepper and sprinkle with parsley.