In a Dutch oven or large pot with a lid, heat the olive oil and add the shallot and chopped garlic, season lightly with salt and pepper and cook over medium heat, stirring, until the garlic is softened and barely golden, about 2 minutes. 

Add the chicken broth and bring to a boil then add the mussels and wine, cook for 1 minute, giving it a stir occasionally. Cover with the lid and steam the mussels until they open, about 4-5 minutes. Remove from the heat. Using a slotted spoon, transfer the mussels to 6 serving bowls, discarding any mussels that do not open.

Return the pot to the heat and bring to a boil to reduce the pot broth slightly. Add the butter and parsley to the broth, and stir until the butter melts. Slowly pour the broth over each serving of the mussels. Garnish each serving with a sprinkle of chopped parsley and serve with crusty grilled bread.