Cut the carrots, turnips, and parsnips into pieces of about the same size and shape, preferably a medium-sized dice.
Blanch the cut carrots, turnips, parsnips, and onions together, in a pot of boiling salted water, until tender, about 5 minutes or less. Carefully remove from the blanching water with a slotted spoon and place into an ice water bath. Allow vegetables to cool; reserve in refrigerator until you are ready to serve them.
To serve, put the vegetables in a small skillet along with sherry vinegar, butter, and chopped tarragon. Place the skillet over a medium-low flame and warm just moments before serving. Season with salt and pepper.