I realize that most people who avoid egg yolks, eating only the whites, are looking to conserve calories and eat healthfully. I make egg white omelets for a different reason: egg whites are a blank canvas and leave room for the flavors and textures of herbs and cheese to truly shine. Be sure to use the freshest eggs you can find, because fresh egg whites are denser and cook up heartier than thin older whites. In this omelet, the egg white takes the tarragon and Parmesan and runs with them. By the way, this omelet can easily be made without the cheese and with the addition of roasted mushrooms or cherry tomatoes. I like the "lean" egg white mingling with the rich cheese.
Prepare the egg whites: In a bowl, whisk the egg whites with the salt and a pinch of pepper. Whisk only enough to integrate the eggs. You don't want to whip too much air into them or make them frothy.
Cook the omelet: Place a 6-inch nonstick skillet over medium heat and add the butter. Swirl the butter around as it melts so it coats the whole surface of the pan. When the butter is melted (but not browned), reduce the heat and pour in the egg whites. Use a fork to stir the eggs slightly, as if you were scrambling them. Then allow the eggs to cook undisturbed for 1 to 2 minutes. Sprinkle the tarragon and cheese over the eggs, and then squeeze a little juice from the lemon wedge over the top.
Finish: Lift the handle of the pan up, tilting the pan away from you and toward the heat. Fold the edge of the omelet closest to you toward the center. Fold the other edge toward the center and tilt the pan over the center of a plate so it lands seam-side down. Butter the omelet, if desired. Serve immediately.