Melt the butter over low heat in a large pot. Add the anchovies and let them sit on low heat for about 15 minutes, until the anchovies have also melted into the butter.
Rinse and sort the mussels. Discard any that don’t close when you wash them.
Add the good mussels to the pan with the butter and anchovies. Turn the heat up slightly (to medium), cover with a lid, and let them steam for 10 minutes.
Finely chop the dill and add it to the pan once all the mussels have opened. Discard any mussels that stayed closed — they’re not good.
Slice your baguette.
Scoop the mussels into a serving bowl and pour the cooking liquid into a small bowl or jug to use as a dipping sauce for the baguette.