Put the potatoes in a saucepan with enough water to cover by 2 inches. Bring the water to a boil and cook the potatoes until tender, 15 to 20 minutes. Drain and let cool for 5 minutes. Peel the potatoes and cut them into chunks. Put in a medium bowl and sprinkle with the vinegar while still warm; season with 1/2 teaspoon salt.
Whisk together the mayonnaise, lemon juice, mustard, sugar, anchovies, garlic and 1 teaspoon salt in a large bowl. Add the potatoes and toss to coat.
Heat the oil in a skillet over medium heat. Add the panko and cook until brown, about 3 minutes. Stir in the parsley.
Transfer the potatoes to a serving dish and sprinkle with the parsley breadcrumbs.
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