Partly fill a large bowl with water and stir in 2 tablespoons salt. Add mussels and more water if needed to cover. Let soak in refrigerator for 1 to 2 hours to purge sand (if mussels are the cultivated rope-raised kind, they may not need treatment).
Dice potatoes in 1-inch pieces. Dice fennel in ½-inch pieces (about 1½ cups). Chop onion. Finely chop garlic.
Heat ¼ cup olive oil over medium heat in a large, heavy-bottomed saucepan. Saute onion until golden. Stir in fennel, garlic, 2 teaspoons salt, bay leaves and red pepper flakes. Cook until vegetables are softened but not browned.
Add tomatoes, breaking them up with a wooden spoon (alternatively, puree tomatoes with their puree in a blender). Simmer for 10 minutes or so. Add potatoes and enough water to barely cover. Continue to cook, with lid ajar, until tender.
Add mussels and cooking liquid to saucepan with stew if there’s room; if not, combine liquid with stew and leave mussels in skillet.
Taste broth and add more salt and red pepper flakes if needed.
To serve: Spoon stew into broad, shallow bowls. Top each serving with several mussels and sprinkle with parsley.
• Choose good-quality canned Italian tomatoes such as San Marzano. For a thicker stew base, add a couple tablespoons of tomato paste to the stew base. If fresh tomatoes are in season, you could substitute several for canned tomatoes; peel, seed, dice fresh tomatoes before adding to the stew.
• Fresh shrimp are great, but as a time saver, I sometimes use individually frozen wild shrimp. Unless thawed first, they need a little extra cooking.
• If using canned beans, drain and rinse them before adding. Beans cooked from scratch are even better; you can add some of their cooking liquid to the stew base.
• The easy path to a richer-tasting broth is to add a small bottle of clam juice to the stew base. A more labor-intensive but more flavorful route is to make broth from heads and frames of mild-tasting fish; strain and substitute for water called for in recipe.
*For a bright finish, stir in zest of 1 tangerine or orange just before serving.