How to Make It
In a large bowl, cover the mussels with cold water. If they are sandy, rub them against one another. Transfer the mussels to another bowl of cold water. Repeat the process, rinsing out the bowl each time, until there is no sand left.
Transfer the mussels to a large nonreactive pot and add the wine and 1/2 cup of water. Cover and bring to a boil. Cook the mussels, tossing occasionally, for about 7 minutes. As the mussels open, transfer them to a bowl; discard any that do not open. Slowly pour the mussel cooking liquid into a bowl, leaving any grit behind. Reserve the liquid in the refrigerator for another use. Let the mussels cool, then remove them from their shells, discarding any remaining beards, and transfer to another bowl.
Meanwhile, in a medium saucepan, cover the potatoes with cold water and bring to a boil over high heat. Reduce the heat to low and boil gently until tender, about 20 minutes. Drain the potatoes and let cool slightly. Slice the lukewarm potatoes crosswise 1/4 inch thick. Add the potatoes and scallions to the mussels in the bowl.
In a small bowl, combine the garlic, vinegar, mustard, oil, salt and pepper. Add the dressing to the mussels and toss gently. Arrange the salad greens on 4 plates and spoon the salad on top. Serve warm or at room temperature.