Run the mussels under cold water and clean them, removing the beards and discarding any that should not be cooked.
Pour 1/2 cup water into a large pot and add the salt. Place the lovage sprigs on top with the stem ends facing down, then add the mussels. Leave about 2-3 inches of space between the mussels and the top of the pot. Cover and cook until the mussels open - usually around 7 minutes for this recipe, but watch the mussels rather than relying only on the clock.
Remove the mussels and strain the cooking liquid well. Discard the cooked lovage and reserve all of the strained liquid.
Set aside about 25 mussels in their shells. Remove the meat from the remaining mussels and set it aside separately.
Wash and drain the rice. Finely chop the onion, carrots, and green pepper. Remove the seeds from the tomatoes and grate them, discarding the skin left on the grater.
Heat the olive oil in a large saucepan and saute the onion for 5 minutes.
Add the rice and cook for no more than 1 minute.
Immediately stir in the carrots, green pepper, and grated tomatoes. Measure the reserved mussel cooking liquid and add enough water to make 3 cups total. Pour the liquid into the pan and season with the black pepper.
Add the reserved mussels in their shells and stir them through the rice. Cover, reduce the heat, and simmer for 10 minutes without opening the lid or stirring again. As the rice begins to swell, some of it will work its way inside the open shells.
Add the reserved mussel meat and stir again to distribute it through the rice. Cover and cook for another 7-8 minutes. Taste the rice toward the end - it should be cooked through but the grains should remain distinct rather than becoming mushy.
Remove the pan from the heat, stir in the fresh parsley, cover, and let the dish rest for 15 minutes. The rice will continue absorbing some of the remaining liquid as it rests.
Serve warm, garnished with parsley and a lemon wedge if desired. We sometimes use an empty mussel shell instead of a fork to scoop up the rice.