Wash and dry all produce. Preheat broiler or grill to high or oven to 500 degrees. Trim, then thinly slice scallions, keeping greens and whites separate. Cut potatoes into 3/4-inch pieces. Trim any stems from green beans, then cut 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 medium bowl, keeping pot of boiling water on stove. Place bowl in refrigerator to cool potatoes.

Line a baking sheet with aluminum foil and lightly oil. Place chicken on sheet. Season with salt and pepper. Brush tops with half the barbecue sauce. Broil, bake, or grill until charred in spots, 5-7 minutes. Flip and brush with remaining barbecue sauce. Broil or bake until no longer pink, 7-10 minutes. TIP: Skip sheet if using grill, adding sauce during last 2 minutes of grilling.

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 2 tsp white wine vinegar (we sent more) to bowl with potatoes. Toss to combine. Season with salt and pepper.

Divide potato salad between plates. Top with chicken. Garnish with scallion greens and serve.