Mix eggs and egg whites in a bowl with turkey, tarragon, and salt and pepper. Set aside.
Spray a nonstick pan with olive oil and place over high heat. Saute mushrooms and tomatoes for 2 minutes and remove.
Pour in the egg mixture. Let the eggs set for about 30 seconds. Tip the pan and lightly move the eggs so that they set completely. Cook for 1 1/2 minutes or until eggs are set.
Place the mushrooms and tomatoes on half the omelette and fold the omelette in half. Slide out of the pan by tipping the pan and holding a plate vertically against the side of the pan. Turn pan and plate to invert the omelette on to the plate.