Trim and discard the dark green tops and tough outer leaves from the leeks. Remove the roots along with a very thin slice of the nearby white part. Halve the leeks lengthwise and wash them under cold, running water. Gently spread apart but do not separate the inner layers to remove all traces of soil. If the leeks are particularly sandy, soak them in several changes of clean water.
Bring several inches of water to a boil in large saucepan. Place the leeks in a single layer in a steamer basket and place the basket in the pan. Cover the pot and steam until the leeks are tender, about 15 minutes. Remove the leeks from the steamer basket and transfer to a platter. Pat dry with paper towels. (The leeks may be cooled slightly or covered and refrigerated until well chilled.)
While the leeks are steaming, whisk the vinegar, mustard, and salt and pepper to taste together in a small bowl. Whisk in the oil until the dressing is smooth. Whisk in the tarragon and adjust the seasonings.
Drizzle the dressing over warm or chilled leeks and serve immediately.