Bring a large pot of salted water to a boil over high heat. Add the halved baby potatoes and cook until they are easily pierced with a fork, about 10 to 12 minutes. During the last 3 minutes of boiling, toss the trimmed green beans into the same pot to cook until they are tender-crisp.

While the vegetables cook, prepare a large bowl filled with cold water and ice cubes. Use a slotted spoon to transfer the cooked potatoes and green beans directly into the ice bath to stop the cooking and lock in their bright colors. Drain them well after 2 minutes and pat dry with a clean towel.

Gently lower the eggs into the same pot of boiling water and cook for exactly 7 minutes for slightly jammy yolks, or 9 minutes for traditional hard-boiled eggs. Transfer the eggs to the ice bath to cool completely before peeling and cutting them in half lengthwise.

Whisk together the extra virgin olive oil, red wine vinegar, Dijon mustard, and chopped parsley in a small bowl until the mixture emulsifies into a smooth vinaigrette. Season the dressing with a pinch of salt and freshly ground black pepper to taste.

Arrange the potatoes, green beans, halved cherry tomatoes, olives, and capers beautifully on a large serving platter. Flake the drained tuna over the top in generous chunks, nestle the egg halves into the gaps, and drizzle the vinaigrette evenly over everything right before serving alongside some warm crusty baguette.