Slice the potatoes 1/3-inch thick and put in a saucepan with 1 teaspoon of the salt, the water, and the wine. Tie the parsley stems, peppercorns, and thyme in a piece of cheesecloth and add to the pot. Bring the liquid to a boil over high heat and immediately lower the heat to maintain a simmer. Cook until the potatoes are tender but not mushy, about 12 minutes. Drain; discard the herb bundle and transfer the potatoes to a bowl. While the potatoes are cooking make the dressing. In a small bowl, whisk together the vinegar, shallots, the remaining 2 teaspoons of the salt and pepper. Gradually whisk in the oil to make a dressing. Toss the warm potatoes with the dressing gently so as not to break up the potatoes. Allow the salad to sit at room temperature for one hour to marinate, tossing several times to coat the potatoes. Add the parsley. Season with salt and pepper to taste. Serve at room temperature.
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