Prepare Hard-Boiled Eggs: Place eggs in a medium saucepan, cover with water, bring to a boil, then remove from heat and cover for 10 minutes. Transfer to cold water to cool.

Cook Potatoes: Rinse new potatoes, cut small ones in half, place in a large pot with salted water, and boil for 12 minutes or until fork-tender.

Add Green Beans: Trim and cut green beans into thirds; after 12 minutes of cooking potatoes, add them to the pot and cook for an additional 2 to 3 minutes.

Shock in Ice Bath: Transfer the cooked potatoes and green beans to a bowl filled with ice water for 5 minutes to cool.

Make Vinaigrette: In a jar, combine olive oil, lemon juice, white wine vinegar, minced garlic, Dijon mustard, capers, and olives. Shake vigorously until well mixed.

Assemble Salad: In a large bowl, mix parsley and chives with half the vinaigrette, add cooled potatoes and green beans, toss gently, and top with quartered hard-boiled eggs.

Drizzle remaining vinaigrette on the salad before serving to enhance flavors.