Step 1

Cover potatoes with 3 qt. water in a large saucepan. Stir in ½ cup salt. Bring to a simmer over medium-high heat. Reduce heat to medium and continue to simmer until potatoes are just tender when pierced with a skewer or paring knife, about 12 minutes. Drain and let cool slightly.

Step 2

Meanwhile, prepare a grill for medium heat. Whisk vinegar, fish sauce, honey, and 3 Tbsp. oil in a small bowl. Stir in chiles. Season dressing with salt; set aside.

Step 3

Cut onion in half through the root, then cut each half into 5 wedges so that they’re still held together by the root.

Step 4

Finely grate garlic into a large bowl. Whisk in ¼ cup oil. Add onion wedges to bowl. Smash potatoes lightly with your hands as you add them to bowl, tossing gently to coat with garlic oil. Season with salt.

Step 5

Grill potatoes and onion wedges, turning occasionally, until charred all over, 12–15 minutes. Wipe out bowl you tossed the potatoes in, then return potatoes and onions to bowl when they’re finished grilling.

Step 6

Pour dressing over potatoes, tossing to coat. Add basil (tearing any large leaves in half) and sesame seeds. Taste and season with salt if needed, then toss again to combine.

Step 7

Transfer potato salad to a serving bowl. Drizzle with oil.