Place the potatoes and salt in a large saucepan and add 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, about 5 to 6 minutes. You should be able to slip a paring knife in and out of the potatoes with little resistance.

Thread the garlic cloves onto a small skewer while the potatoes cook. Lower the skewer into the simmering water for 45 seconds to blanch the garlic, then rinse under cold running water before mincing the cloves fine.

Drain the potatoes, reserving a small amount of the cooking water. Arrange the hot potatoes close together in a single layer on a rimmed baking sheet.

Whisk the oil, minced garlic, vinegar, mustard, pepper, and the reserved potato cooking water in a bowl until emulsified. Drizzle the dressing evenly over the hot potatoes and let them sit at room temperature for 10 minutes to allow the flavors to meld.

Transfer the potatoes to a large bowl. Combine the shallot and herbs in a small bowl, then sprinkle them over the potatoes and fold gently with a rubber spatula to combine. Serve warm or at room temperature.