Start by bringing a large pot of water to a boil for the potatoes, and simultaneously boil the room temperature eggs in a separate smaller pot of water. After 1 minute, remove the eggs from heat, cover, and let sit for 10 minutes to cook through gently—this ensures creamy yolks without the gray ring. While the eggs rest, add the potatoes and 1.5 tbsp salt to the boiling water and cook for 12 minutes until just tender. The eggs and potatoes will finish at roughly the same time, creating an efficient workflow.
When the potatoes have cooked for 12 minutes, add the green beans to the same pot and continue cooking for 2–3 minutes until bright green and tender-crisp. At the same time, peel and quarter the rinsed eggs. Immediately drain the potatoes and green beans, then transfer them to a bowl of ice water to stop the cooking and set their color—this prevents them from becoming mushy and keeps the vegetables vibrant.
While the vegetables chill, prepare the dressing by mincing the garlic cloves finely and combining them with the olive oil, lemon juice, white wine vinegar, Dijon mustard, capers, 1 tbsp black olives, 1/2 tsp salt, and 1/2 tsp black pepper in a jar. Shake vigorously for 30 seconds until the mustard emulsifies and the flavors bind together. I find a true French vinaigrette benefits from good-quality California olive oil and fresh lemon juice—these make a noticeable difference in the final taste.
Drain the chilled potatoes and green beans from the ice water and transfer them to a large bowl. Add the parsley sprigs and chives to the vegetables along with the 15 black olives, then pour half the vinaigrette from Step 3 over everything and toss gently to combine. The warm vegetables will absorb the dressing beautifully while the herbs release their fresh flavor. I like to add fresh herbs just before dressing rather than earlier—this keeps them vibrant and aromatic.
Arrange the quartered eggs from Step 1 on top of the salad—this creates a beautiful French presentation and keeps them from breaking apart during tossing. Drizzle the remaining vinaigrette over the eggs and the salad. Serve immediately while the potatoes and beans are still warm, as this is when the flavors meld most beautifully.