1. For the pesto, make a paste with the basil, garlic, and olive oil by pounding with a mortar and pestle or pureeing in a blender. Press plastic wrap directly onto the pesto and refrigerate, (The pesto can be made 1 day before serving.)

2. For the beans, place all the ingredients in a medium saucepan. Bring to a boil, lower the heat slightly, and simmer until tender, about 30 minutes. Drain and discard the aromatics. Refrigerate the beans.

3. For the mussels, place the olive oil, garlic, shallot, and parsley in a large, wide pot over medium heat. Cook until the garlic and shallot are softened, about 2 minutes. Add the wine and mussels, cover the pot, and raise the heat to high. Cook, stirring occasionally, until the mussels are opened, about 5 minutes. Strain and reserve the mussel broth. Shell the mussels, discarding any that did not open. Refrigerate.

4. For the vegetables, measure the mussel broth and add fish fumet, if necessary, to make 2 cups. Place in a medium saucepan with 2½ cups additional fish fumet. Add the carrots, fennel, and zucchini and bring to a boil. Lower the heat and simmer, skimming off the foam as it rises, until the vegetables are tender, about 12 minutes. (The recipe can be made to this point several hours ahead; refrigerate vegetables and broth.)

5. To serve, stir the tomato and the beans into the vegetables and broth. Bring to a boil. Stir in the pesto and remove from the heat. Divide the mussels among 4 soup bowls. Ladle the soup over the mussels, making sure the beans and vegetables are evenly distributed. Squeeze lemon juice over the top and serve immediately.