In a large bowl, combine 4 cups water with 3 tablespoons salt and stir to dissolve the salt. Add the mussels and let stand for about 1 hour to rid the mussels of any bits of sand, then drain well. Place the mussels in a clean bowl and refrigerate, uncovered, for up to 1 day.
Preheat the oven to 375 degrees F (190 degrees C). Arrange the mussels in a single layer in a shallow baking pan, discarding any that do not close to the touch, and add the shallots and wine. Cover the pan with aluminum foil and bake just until the shells open, about 10 minutes. Remove the mussels from the oven and let cool in the pan. Remove the mussels from the wine, discarding any that failed to open, and discard the wine (or strain through a fine-mesh sieve and reserve for adding to a fish soup or stew). Increase the oven temperature to 400 degrees F (200 degrees C).
Meanwhile, in a food processor, process the bread pieces until they form coarse crumbs. Measure out 1 cup and set aside; reserve the remainder for another use.
Working with one mussel at a time, pull off and discard the top shell and run a small, sharp knife around the mussel meat to free it from the bottom shell. Lay the mussels, still in their bottom shells, in a single layer in the baking pan. Spoon an equal amount of the green garlic butter (Traditional French Green Garlic Butter With Pastis
, optional) onto each mussel and sprinkle the crumbs generously on top.
Return the mussels to the oven and bake until the tops are sizzling, the butter is melted and fragrant, and the crumbs are crisp, about 8-10 minutes.
Transfer to a platter and serve at once, with the lemon wedges on the side.
Good with a crisp, chilled white wine such as Muscadet or Sancerre!
Note: Makes six servings as an appetizer, or about three main dish servings.