Heat oil in skillet or non-stick saute pan over medium heat.
Beat eggs until they reach a pale yellow color. Add Dill weed, Tarragon, pepper, and salt. Whip egg mixture some more to make nice and frothy. The goal is to introduce as much air as possible.
Pour egg mixture into pan. As eggs start to set, gently lift the sides with a rubber spatula and tilt skillet to allow liquid to run underneath until no liquid is left.
Once eggs are set, add chopped tomato, turkey breast, and cilantro to one side of omelet, and cover by lifting other side of omelet up and over with rubber spatula.
Cover skillet and cook for 1 more minute. Flip omelet, cover, and cook another minute. Be careful not to let the eggs turn brown.
Cut in half and serve on two plates. Garnish with fresh cilantro, if desired.
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