Prepare hard-boiled eggs by placing cold eggs in a saucepan covered with water, bring to boil, let boil for 1 minute, cover and let sit for 10 minutes, cool under running water, peel and slice into quarters.

Cook new potatoes by halving them and boiling in salted water for approximately 12 minutes until tender but firm.

Add green beans to the pot with the potatoes in the last 2-3 minutes of boiling until bright green and crisp-tender.

Transfer cooked potatoes and green beans to an ice bath for 5 minutes to stop cooking and maintain color.

Make the vinaigrette by combining olive oil, lemon juice, vinegar, garlic, mustard, capers, and olives in a jar, season with salt and pepper, and shake until emulsified.

Combine parsley, chives, half of the vinaigrette with the cooled potatoes and green beans, and toss gently to coat.

Serve the salad mixture on a platter topped with quartered hard-boiled eggs, drizzle with remaining vinaigrette, and season before serving.