In a small saucepan, combine Jerusalem artichokes, tarragon stems, and half of the vinegar. Add enough water to cover by about 1/2 inch. Season with salt and pepper. Bring to a boil over high heat, reduce to a simmer, and cook until tender, about 25 minutes. Drain, and place in a blender. Add just enough of the cooking liquid to puree until very smooth. Add reserved tarragon leaves, remaining vinegar, and shallots. Pulse to combine. Add either grapeseed oil or a little of the cooking liquid depending on the desired consistency.