In small bowl, beat together eggs, water, salt and pepper, if desired, until blended. In a skillet over medium-high heat, heat butter until just hot enough to sizzle a drop of water. Pour in egg mixture. Mixture should set immediately at edges.
With inverted pancake turner, carefully push cooked portion at edges toward center so uncooked portions can reach hot pan surface. Tilt pan and move cooked portions as necessary.
When top is thickened and no visible liquid egg remains, fill with 1/3 cup filling ingredients. With pancake turner, fold omelet in half.
Invert onto plate with a quick flip of the wrist or slide from pan onto plate.
