Season a large pot of water generously with salt and boil the potatoes until just tender enough to pierce with a knife. Remove with a slotted spoon.
Then, cook the green beans in the same water until barely tender. Immediately transfer beans to an ice bath to stop cooking.
Meanwhile, whisk together shallots, lemon zest, juice, garlic, vinegar, oregano, dill, honey, and Dijon in a bowl. Season with salt and pepper, then slowly stream in olive oil.
Slice potatoes lengthwise, then toss in a large bowl with the green beans, dressing, capers, and olives.
Adjust seasoning, transfer to a serving dish, and finish with fresh dill and cracked pepper.
