Bring 1 inch of water to a boil in a large saucepan fitted with a steamer basket. Add potatoes to the basket; cover and steam until tender, 10 to 12 minutes. Transfer the potatoes to a medium bowl. Add vinaigrette and toss gently with a flexible spatula to coat. Let the potatoes stand in the dressing for a minute or two. Using a slotted spoon, transfer the potatoes to a platter or divide between 2 plates.
Add green beans to the steamer basket, cover and steam until tender-crisp, 4 to 6 minutes. Rinse under cold running water to stop the cooking.
Arrange the green beans, chickpeas, tomatoes, tuna, and eggs on the platter (or plates). Drizzle the remaining dressing from the bowl over the salad. Garnish with parsley, if desired.
Easy Anchovy Vinaigrette