Heat oil or margarine in large pot over medium heat. Add onion; Sauté until soft, about five minutes.

Add parsnips, potatoes, and turnips; stir five minutes. Add garlic; stir one minute. Add chicken soup; bring to a boil.

Cover; reduce heat to medium-low. Simmer until vegetables are tender, about 15–20 minutes.

Using slotted spoon, transfer vegetables to large bowl; reserve soup. Add mayonnaise to vegetables.

Using a potato masher, mash vegetables to a smooth puree. Add two tablespoons soup to pureed vegetables. You may add additional soup, to reach desired creamy consistency.

Season with salt and pepper.