Place eggs in a saucepan, cover with cold water, and bring to a rolling boil over medium heat. Cook for 10 minutes, then transfer to an ice bath.

In a large pot, bring salted water to a boil and add halved new potatoes. Cook until tender, about 12 minutes, then drain and cool slightly.

Toss trimmed green beans into the pot with the potatoes and simmer for an additional 2-3 minutes. Drain and transfer to an ice-water bath.

In a jar or bowl, combine olive oil, lemon juice, white wine vinegar, minced garlic, Dijon mustard, capers, and olives. Season to taste and whisk or seal and shake until emulsified.

In a large bowl, combine chopped herbs with half of the vinaigrette. Add cooled potatoes and green beans, incorporating the remaining olives. Toss lightly.

Fold in quartered boiled eggs, drizzle with remaining vinaigrette, and gently toss before letting sit for a moment to meld flavors.