Place mussels in a large bowl with cold water to cover. Tap each mussel on the counter as you do; discard any shells that fail to close. Let them soak for about 20 minutes to remove any dirt or sand.
Heat olive oil and butter in a large stockpot over medium-low heat. Add garlic and saute until fragrant, about one minute, but do not brown. Add the wine and chicken broth, and simmer briskly until reduced by half. Add the tomatoes and cook 4-5 minutes, until nearly tender.
Drain mussels and add to pot. Cover and simmer briskly 5 minutes. Add the scallion and parsley. Re-cover and simmer another 5 minutes, until all the shells are open. Season with salt and pepper to taste. Discard any shells that fail to open.
Serve each diner 8 mussels with a good ladle of the sauce and plenty of crusty bread to mop it up.