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Step 1
Clean the mussels in cold running water and discard any that remain open or have cracked or damaged shells.
Step 2
Place a saucepan over medium-high heat and wait for it to get hot before pouring in the mussels, wine, and stock. Add the bay leaves, parsley, star anise, peppercorns, and lemon, and add a tight-fitting lid immediately.
Step 3
Steam the mussels for a few minutes until they are all open, then strain them through a sieve, retaining the cooking liquid in a bowl underneath.
Step 4
Place the mussels in a bowl covered with foil.
Step 5
Return the saucepan to the stovetop over medium heat and add the butter and oil.
Step 6
Saute the diced shallot and garlic until translucent, then add the reserved cooking water. Reduce the volume by half over high heat.
Step 7
Pour in the cream and reduce the volume by one third over high heat. Sieve the mussels soup to remove the shallot and garlic and return to the saucepan over low heat.
Step 8
Whisk in another tablespoon of butter and a squeeze of lemon juice. Season to taste with salt and pour into shot glasses to serve.
Step 9
Top each amuse bouche with a mussel, and loosen it from its foot first to make it easier fo guests to eat from the shell.