Step 1Heat the oven to 325 degrees. Rinse the duck legs and pat them dry. Season them well on both sides with the salt and pepper and lay them in an oiled, shallow baking dish. Sprinkle with thyme and arrange the garlic cloves around. Roast 1 hour. Opening the oven briefly, pour the wine or vermouth carefully around the legs, avoiding the skin. Continue roasting until the meat is very tender, about 30 minutes longer. Set aside to cool slightly.
Step 2While the duck cooks, place the potatoes in a large pot of salted water and bring to a rolling boil. Reduce the heat and simmer until just tender, about 25 minutes. Drain well.
Step 3While the potatoes cook, whisk together the mayonnaise, mustard, vinegar, shallots, cornichons, capers, chives, dill and basil. Season with salt and pepper to taste.
Step 4Thinly slice the still-warm potatoes on the diagonal and place in a large bowl. Pour the dressing over them and toss to coat. Shred the duck meat with two forks into large chunks and add to the bowl (discard the skin if it's too tough). Toss again. Taste and adjust the seasoning. Arrange on the frisee, romaine leaves or arugula; sprinkle with a good handful of the chopped chives and serve warm.