Trim leeks, slice in 1/2 lengthwise and rinse to remove sand and dirt. Cut them about 4-in long and place in a steamer basket and steam about 10 minutes, until tender, and set aside on paper towels for 20 minutes.
Beat the egg, pepper, and half of the tarragon together in a bowl.
Heat just enough oil to cover bottom of pan until a drop of water will sizzle in the pan.
Coat the leeks in the eggs, then flour, and fry until browned, turning often.
Sprinkle with vinegar and rest of tarragon and serve.