Trim beets, leaving 1 inch of stems attached. Cover beets with cold water by 2 inches in a 5- to 6-quart pot and boil, uncovered, until tender, 40 to 45 minutes (adding more water if necessary). Drain beets and let cool. Cut stems from beets with a small sharp knife, then peel and discard skin from beets. Cut beets into wedges.
Mound mache alongside beets on a platter and drizzle with vinegar and oil. Sprinkle both with tarragon and kosher salt and pepper to taste. Serve at room temperature.