Clean mussels under cold running water. With a sharp knife remove beard (the thread like fronds) and discard together with any open mussels that don't close when tapped.
Melt butter in a large pan, add garlic and onion. Sweat for 5 minutes — don't brown.
Chop fennel, reserving feathery tops for garnish, and add to pan with mussels, wine, stock and bay leaf. Increase heat, cover with lid and cook for 5 minutes, stirring halfway through.
The mussels are cooked when all the shells are open. Discard any that remain closed. Serve in big bowls.
We recommend pairing this simple, aromatic moules marinière with finest* Pecorino Terre Di Chieti white wine.