Preheat the grill to medium. Boil the potatoes in salted water just until almost tender, about 8 minutes. Remove to a bowl of ice water to stop the cooking. Slice the cooled potatoes into 1/2-inch rounds. Brush both sides of the potato slices with oil and place on the grill just until nice grill marks form, about 3 minutes per side.
In a small bowl, stir together the remaining olive oil, parsley, chives, tarragon, garlic, lemon zest and juice. To serve, shingle the potatoes so that 1 piece overlaps the next. Sprinkle the potatoes with salt and generously spoon the herb salad over the top.