In a medium pan of boiling water to cover, cook the potatoes until tender, but not soft, 12 to 16 minutes, depending on the size of the potatoes.
Cool under running water, peel, and cut into 3⁄4-inch cubes.
Put into a large bowl and set aside.
Cook the carrots, cauliflower, and green beans, each separately, uncovered, until crisp-tender.
The carrots take about 4 minutes, cauliflower about 3 minutes, and the green beans about 6 minutes.
Rinse each vegetable through a sieve under cold running water to stop the cooking.
Shake excess water.
Put the cooked vegetables in the bowl with the potatoes.
Add the salt and olive oil, and toss gently.
Cover and refrigerate until the vegetables are cold, at least 1 hour.
Remove the vegetables from the refrigerator shortly before serving and add the tomatoes.
Toss the salad with sufficient vinaigrette to coat generously.
Line a shallow bowl or serving platter with the romaine leaves.
Mound the vegetables on the lettuce.
Serve cold.