1. Heat the broiler. Put the mushroom caps on a baking sheet. In a small bowl, combine the 1/3 cup oil, 1 teaspoon of the thyme, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Pour the mixture over the mushrooms and toss to coat. Broil the mushrooms, turning once, until tender and golden, 6 to 8 minutes per side.
2. Meanwhile, put the potatoes in a medium saucepan of salted water. Bring to a boil and simmer until tender, 5 to 10 minutes. Drain.
3. In a small glass or stainless-steel bowl, mix together the mustard, vinegar, and the remaining 1/4 teaspoon thyme, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Add the 6 tablespoons oil slowly, whisking. Toss the warm potatoes with 2 tablespoons of the dressing.
4. In a large bowl, combine the scallions, watercress, and curly endive. Toss with the remaining dressing and then put the greens on a platter or individual plates. Scatter the warm dressed potatoes over the greens. Slice the mushrooms and serve on top of the salad.
Wine Recommendation: Wines made from the sémillon grape are rich, full-bodied, and intense, and yet they are surprisingly compatible with a number of cuisines. Look for one from the Hunter Valley of Australia for an interesting and tasty accompaniment for this salad.