Prepare Hard-Boiled Eggs: Place the eggs in a saucepan, cover with cold water, bring to a boil, cover, turn off heat and let sit for 10 minutes. Cool under running water, peel, and quarter.

Cook Potatoes: In a large pot, add halved new potatoes and enough salted water to cover. Boil for about 12 minutes until tender but firm. Drain and cool slightly.

Add Green Beans: With potatoes in the pot, add trimmed green beans and cook for another 2-3 minutes. Drain immediately.

Ice Bath: Transfer potatoes and green beans to a bowl of ice water for 5 minutes to stop cooking, then drain.

Make Vinaigrette: Combine olive oil, lemon juice, vinegar, minced garlic, mustard, capers, and seasoning in a jar or bowl. Shake or whisk until emulsified.

Combine Ingredients: In a mixing bowl, combine cooled potatoes, green beans, parsley, chives, and olives. Add half the vinaigrette and toss gently.

Serve: Top with quartered eggs and drizzle with remaining vinaigrette. Allow resting for at least 30 minutes before serving.