Place potatoes and 1/2 teaspoon salt in a Dutch oven; add water to cover. Bring to a boil. Reduce heat; cook, uncovered, until tender, 10-12 minutes. Drain and cool.
Mince white portions of green onions; slice green portions and reserve. Combine minced onions with celery, red onion and carrot. For dressing, whisk together vinegar, honey, mustard, thyme, sea salt and coarsely ground pepper. Gradually whisk in oil until blended.
Cut cooled potatoes into 1-inch pieces, preserving as much peel as possible. Combine potatoes with onion mixture. Drizzle dressing over salad; toss to coat. Top with reserved green onion slices.