Prepare Hard-Boiled Eggs: Place eggs in a saucepan and cover with cold water. Bring to a boil, then simmer for 1 minute. Remove from heat, cover, and let sit for 10 minutes. Cool under cold running water, then peel and quarter.

Cook the Potatoes: Halve or quarter the new potatoes, add to a pot of salted boiling water, and boil for about 12 minutes until tender but firm.

Cook the Green Beans: Add the trimmed green beans to the pot during the last 2-3 minutes of cooking potatoes. They will stay crisp and absorb flavor.

Ice Bath: Drain the potatoes and beans, then immerse in ice water for 5 minutes to halt cooking and preserve color.

Make the Vinaigrette: Combine olive oil, lemon juice, white wine vinegar, minced garlic, and Dijon mustard in a jar. Add capers and olives, season, and shake until emulsified.

Combine the Salad: In a mixing bowl, toss potatoes and green beans with half of the vinaigrette. Add fresh herbs and gently fold together.

Garnish and Chill: Transfer to a serving platter, top with quartered hard-boiled eggs, drizzle with remaining vinaigrette, and chill for at least 1 hour.

Serve and Enjoy: Toss salad before serving. This salad can be enjoyed chilled or at room temperature.