In food processor, combine egg yolks, vinegar, mustard, salt and pepper. Cover and process until well mixed. With motor running, drizzle oil through the feed tube in a thin stream. Process just until all oil is added. Dressing should emulsify and thicken as oil is added.
Cook whole unpeeled potatoes in boiling water with cover with 1 teaspoon salt until fork- tender. Drain and let cool to room temperature. Trim ends from beans and cut in half crosswise. Cook beans in boiling water with remaining salt just until crisp tender, about 8 minutes.
In large bowl, combine cooled potatoes, cut into 1/2 inch slices, beans, walnuts, onions, parsley, dressing, and pepper to taste. Toss well. Arrange lettuce leaves on serving platter; top with salad. Serve at room temperature. Makes 6 servings. Enjoy!
*Note: If you are concerned about eating raw eggs, you can buy pasteurized eggs at some grocery stores, but they are a little more difficult to find.