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