Trim the Jerusalem artichokes of any excessively dark or knobby spots and slice thinly. Combine with the next 5 ingredients in a mixing bowl.
Combine the dressing ingredients in a small bowl and stir together. Pour about half over the salad and toss well; reserve the rest. If time allows, let the salad marinate for an hour or two. Stir it up once in a while.
Just before serving, line a patter with the greens. Mound the Jerusalem artichoke mixture over the greens. Surround the edges of the salad with cherry tomatoes and sprinkle the sunﬂower seeds over the top.
Cover and set aside until needed, or serve at once. Pass around the remaining dressing in a small bowl should anyone want more on their salad.