Cover potatoes by 2 inches of water in a medium saucepan; add coarse salt. Bring to a boil, reduce to a simmer, and cook until just tender, 10 to 15 minutes. Drain. Potatoes can be stored in refrigerator up to 1 day.
Preheat grill to medium-high. Toss potatoes with oil in a bowl, then place on grill and cook, turning occasionally, until very tender and marked, about 5 minutes. Toss with sea salt and oregano; serve warm with herb sauce.