Trim the leeks. Cut off the roots but leave enough so that the leaves remain joined at the base. Slice them in half lengthwise down to the base but not through it, and rinse them well. Steam them over boiling water until they are tender when pierced with a knife, about 10 minutes, then set on a towel to cool and drain dry. Beat the egg on a plate and season with salt and pepper. Add the parsley and half the tarragon. Dip the leeks into the egg and slosh them around so that they are well covered, then dip them in flour to coat.

Heat enough oil in a heavy pan to cover the bottom generously. When it is hot enough to sizzle a drop of water, add the leeks. Fry them, turning them frequently until they're nicely browned all over. Set them on a towel to drain briefly. Serve with the remaining tarragon sprinkled over the top and a cruet of vinegar on the side.