Place leeks, cut side up, in one layer in a large straight-sided skillet. Add chicken stock and tarragon, and bring to a boil over high heat. Add butter, reduce the heat to medium, and simmer. Cook until leeks are tender when pierced with the tip of a knife, 10 to 12 minutes. Carefully remove leeks from skillet, and place on a platter; set aside. Strain cooking liquid through a fine-mesh sieve. Measure 1/4 cup liquid, and set aside. Reserve remaining liquid for another use or discard.
In a small bowl, whisk together vinegar and mustard. Add oil gradually while whisking constantly. Whisk in 1/4 cup leek liquid. Season with salt and pepper. Spoon over leeks. Garnish with chopped herbs. The leeks may be served hot or chilled.