Rinse mussels thoroughly under cold running water, removing any dirt or barnacles. Discard any mussels that are broken or remain open when firmly pressed.

Heat olive oil in a large pot with a tight-fitting lid over medium heat. Add shallots and garlic, cooking for 1 to 2 minutes until softened and fragrant.

Pour in the white wine and bring to a rapid simmer. Add the mussels all at once and cover immediately with the lid.

Steam for 3 to 4 minutes, shaking the pot occasionally, until all mussels have opened. Discard any that remain closed.

Remove opened mussels to a large serving bowl with a slotted spoon. Add butter and parsley to the wine broth, swirling until the butter melts.

Pour the aromatic broth over the mussels and serve immediately with crusty baguette for dipping.