How to Make It
Place potatoes in a medium saucepan; cover with salted water, and bring to a boil over high. Reduce heat to medium-high, and simmer until tender when pierced with a knife, 12 to 15 minutes; drain.
Whisk together oil, vinegar, fine sea salt, and pepper; set aside. Cut potatoes into quarters or halves; arrange on a platter in an even layer. Spoon 1/3 cup dressing over potatoes; set aside.
Bring another pot of water to a boil over high. Prepare a bowl of ice water for an ice bath. Cook beans until their color is deeply saturated, about 3 minutes. Remove with a slotted spoon, and plunge into ice water. Drain, and pat dry.
Toss together beans, onion, olives, capers and brine, parsley, and anchovies, if using, with remaining dressing in a large bowl; spread over potatoes. Top with eggs, and sprinkle with flaky sea salt.