Place the eggs in a medium saucepan, cover with water, and bring to a boil. Remove from heat and let sit for 10 minutes. Transfer to an ice bath to cool, peel, and quarter.

Prepare the new potatoes by halving or quartering them for even cooking. In a large pot filled with salted boiling water, cook the potatoes for about 12 minutes until tender but firm. Drain and set aside to cool.

In the pot with the drained potatoes, add the green beans and cook for an additional 2-3 minutes until bright green and tender-crisp. Drain and plunge into ice water to stop the cooking process.

In a jar, combine olive oil, lemon juice, white wine vinegar, minced garlic, Dijon mustard, chopped capers, dry-cured olives, salt, and pepper. Shake until emulsified.

In a large bowl, toss fresh herbs with half of the vinaigrette. Add cooled potatoes, green beans, and olives; mix gently to coat. Arrange quartered eggs on top and drizzle remaining vinaigrette over the dish.

Cover and let the salad chill in the refrigerator for at least an hour or overnight for best results.