Julienne the beets, using a mandoline if you have one. (If you don't, feel free to use a good old fashioned chef's knife.)
In a small bowl, combine the vinegar, oils, salt, and grated ginger. Pour this mixture over the beets and let it sit for an hour or two at room temperature. (You can also refrigerate it for up to a day. The flavors improve with time.)
Immediately before serving, stir in the tarragon and mix well. Enjoy on its own or on top of a bed of greens.