PUT POTATOES IN 3-QUART POT. Cover with water. Add salt and tarragon. Add fresh bratwursts, if using. Bring to boil. Boil, uncovered, until potatoes are almost tender but still with some firmness. Add onions, peas and carrots. Cook 1 minute longer. Drain contents of pot in large, fine strainer. When potatoes are cool enough to handle, cut in half. Split cooked or precooked brats lengthwise, then into 1/2-inch thick slices. Heat oil in 10-inch non-stick skillet over medium-high heat. When hot, add sliced brats. Cook until well browned, about 3 minutes, stirring often. Use slotted spoon to transfer brats to 2-quart mixing bowl. Add potatoes to skillet, cut side down. Cook until browned, about 2 minutes. Use slotted spoon to transfer them to bowl along with sliced green onions and remaining vegetables in strainer. Toss gently to combine.
FOR DRESSING: Add all ingredients to any fat remaining in skillet. Stir well. Heat through but do not boil. Pour over salad. Toss gently to combine. Adjust seasoning. Can be served immediately or refrigerated as long as 1 day. If refrigerated, toss gently to mix ingredients. Adjust seasoning. Can be served at room temperature or warm. If serving warm, reheat gently in non-stick skillet or in microwave oven on medium power (50 %) until warm, not hot. Arrange lettuce leaves on serving plate. Mound potato salad on top. Alternately, salad can be served in shallow soup plates (omit lettuce).