Rinse mussels under cold running water, scrubbing shells to remove grit, discarding any open shells.

Heat olive oil in a large pot over medium heat, sauté shallots and garlic until fragrant, about 2 minutes.

Pour in white wine, stirring to lift any browned bits, then simmer until reduced by half, about 3-4 minutes.

Stir in chicken broth, bring to a gentle simmer, and let flavors meld for 5 minutes.

Increase heat to high, add cleaned mussels, cover pot, and steam until shells open, about 5-7 minutes.

Remove from heat, swirl in cold butter until melted, creating a silky broth.

Transfer mussels and broth to bowls, sprinkle with parsley and serve with crusty bread.