Cover potatoes with cold water in a large pot, bring to a boil. Simmer until slightly resistant in the center when pierced with a small sharp knife. 25-30 minutes. Transfer to a large bowl of cold water to stop the cooking process. Drain well. When cool enough to handle, peel potatoes and slice lengthwise into 4 pieces.
Preheat the grill. When hot, grill potatoes, turning until grill marks appear and potatoes are just tender, 3-6 minutes total. Cut grilled slices of potatoes into cubes. Combine lime juice, salt, pepper, vinegar and add the olive oil in a slow stream to emulsify, whisk in cilantro and drizzle over warm potatoes.
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