Place the potatoes and salt in a large saucepan and add enough water to cover by 1 inch. Bring to a boil over high heat, then reduce the heat to medium-low and simmer until the potatoes are just tender—a paring knife should slip in and out with little resistance—about 5 to 6 minutes.

While the potatoes are simmering, thread the garlic cloves onto a skewer and lower them into the water to blanch for 45 seconds. Rinse the garlic under cold running water, then remove from the skewer and mince fine.

Drain the potatoes, reserving some of the cooking water. Arrange the hot potatoes close together in a single layer on a rimmed baking sheet so they can absorb the dressing without being crowded.

Whisk the oil, minced garlic, vinegar, mustard, pepper, and the reserved potato cooking water in a small bowl until combined, then drizzle evenly over the hot potatoes. Let the potatoes sit at room temperature for 10 minutes to allow the flavors to meld.

Transfer the potatoes to a large bowl and add the shallot and herbs. Use a rubber spatula to combine gently so the potato slices stay intact, and serve warm.