In a steamer, steam whole potatoes over high heat until tender when pierced, 15 to 20 minutes. Remove potatoes as each is done, then steam carrots until just tender, 5 to 7 minutes. Remove carrots and steam pea pods until tender-crisp, about 5 minutes. Transfer to an ice bath to stop cooking, then drain and dry on paper towels.
When potatoes are cool enough to handle (but still warm), halve each lengthwise and transfer to a large bowl. Sprinkle with vinegar and let stand 5 minutes. Halve carrots lengthwise and add to potatoes along with cornichons and pea pods.
In a small bowl, combine yogurt, mayonnaise, salt, and pepper and stir to combine. Pour dressing over vegetables and very gently toss to coat (try not to crush the potatoes). Transfer to a platter and sprinkle with parsley.
Note: Nutritional analysis is per serving.