Step 1

In a large saucepan, combine the potatoes, 2 tablespoons of the vinegar and 2 tablespoons salt. Add enough water to cover the potatoes by 1 inch. Bring to a boil over medium-high, then reduce to medium and cook, uncovered, until a skewer into the potatoes meets just a little resistance, 15 to 20 minutes. Drain the potatoes and return them to the saucepan. Add the oil and ½ teaspoon each salt and pepper, then toss.

Step 2

In a large bowl, whisk together the remaining 3 tablespoons vinegar, both mustards and the herbs; set aside while you prepare a charcoal or gas grill.

Step 3

For a charcoal grill, ignite a large chimney of coals, let burn until lightly ashed over, then distribute the coals evenly over one side of the grill bed; open the bottom grill vents. Heat the grill, covered, for 5 to 10 minutes, then clean and oil the grate. For a gas grill, turn all burners to high and heat, covered, for 15 minutes, then clean and oil the grate.

Step 4

Place a grill basket on the hot side of the grill (if using charcoal). Using a slotted spoon, transfer the potatoes to the basket, distributing them in an even layer; pour the oil remaining in the bottom of the saucepan into the vinegar-mustard mixture. Grill the potatoes, turning occasionally, until evenly browned, about 15 minutes. Transfer the potatoes to the mustard mixture and toss to coat. Taste and season with salt and pepper. Serve warm or at room temperature.