Wash and dry all produce. Trim, then thinly slice scallions, keeping greens and whites separate. Cut potatoes into 3/4-inch pieces. Cut green beans into 2-inch pieces

Place potatoes in a large pot of salted water. Bring to a boil and cook until easily pierced by a knife, 10-12 minutes. Using a slotted spoon, transfer potatoes to a large bowl, keeping pot of boiling water on stove. Place bowl in refrigerator to cool potatoes.

Heat a large drizzle of oil in a large pan over medium-high heat. Season chicken all over with salt and pepper. Add to pan and cook until browned and nearly cooked through, about 5 minutes per side. Add barbecue sauce and reduce heat to low. Cook, tossing to coat chicken, until sauce is thick and glazelike, 1-2 minutes more.

Add green beans to pot with boiling water. Cook until tender but still crisp, 3-4 minutes. Drain, then rinse under cold water. Shake green beans in strainer over sink to dry.

Add green beans, scallion whites, mayonnaise, and 4 tsp white wine vinegar (we sent more) to bowl with potatoes. Toss to combine. Season with salt and pepper.

Thinly slice chicken. Divide potato salad between plates, then top with chicken. Garnish with scallion greens and serve