Step 1Place the mussels in a large, wide pot. Rinse once. Cover them with cold water; shake in 2 teaspoons of salt. Soak 30 minutes, then wash the mussels several times and drain.
Step 2Place the drained mussels over high heat. Cook, covered, until the shells open, shaking the pot occasionally to distribute the heat, about 6 to 7 minutes. Discard any unopened mussels. Line a sieve with a double layer of paper towels; pour off the mussel liquid through the sieve. Reserve any liquid; add enough water to equal 3 cups.
Step 3Melt the butter in a large nonstick skillet over medium heat. Add the shallots and garlic; cook until they're softened and fragrant, stirring often, about 4 minutes. Add the reserved liquid and cream. Bring to boil, then reduce the heat and simmer, uncovered, for about 3 minutes. (This can be made a few hours ahead at this point; refrigerate the mussels in a pot and keep the sauce at room temperature in the skillet.)
Step 4To serve, bring the sauce to a boil, add the tomatoes, all but 2 tablespoons of the parsley, and pepper to taste. Cook 2 minutes. Pour over the mussels in the pot. Cook over high heat, covered, shaking the pot often, until the mussels are very hot, about 2 to 3 minutes. Ladle them into warm bowls, dividing the mussels and liquid evenly and sprinkle with the remaining parsley. Serve immediately with Griddled Bread for dunking.
Step 1Brush the cut side of the rolls with butter. Sprinkle them lightly with salt. About 5 minutes before serving, heat a ribbed griddle or griddle pan. Put the rolls, cut side down, on the hot pan. Cook them until they show grill marks, about 3 minutes. Brush any remaining butter on the tops. Sprinkle them with salt. Use tongs to turn the rolls. Cook the rolls until they're lightly browned, about 2 minutes. Serve them hot.